Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/GAP/pkg/ctbllib/doc2/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 25.4.2025 mit Größe 69 kB image not shown  

Quelle  chap0_mj.html   Sprache: HTML

 
 products/sources/formale Sprachen/GAP/pkg/ctbllib/doc2/chap0_mj.html


<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<script type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (CTblLibXpls) - Contents</title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap0"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chap4_mj.html">4</a>  <a href="chap5_mj.html">5</a>  <a href="chap6_mj.html">6</a>  <a href="chap7_mj.html">7</a>  <a href="chap8_mj.html">8</a>  <a href="chap9_mj.html">9</a>  <a href="chap10_mj.html">10</a>  <a href="chap11_mj.html">11</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap0.html">[MathJax off]</a></p>
<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">

<h1>Computations with the <strong class="pkg">GAP</strong> Character Table Library</h1>

<p>(Version 1.3.11 of CTblLib)</p>

</div>
<p><b>Thomas Breuer
    
    
  </b>
<br />Email: <span class="URL"><a href="mailto:sam@math.rwth-aachen.de">sam@math.rwth-aachen.de</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.rwth-aachen.de/~Thomas.Breuer">https://www.math.rwth-aachen.de/~Thomas.Breuer</a></span>
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2013–2025 by Thomas Breuer</p>

<p>This manuscript may be distributed under the terms and conditions of the GNU Public License Version 3 or later, see <span class="URL"><a href="http://www.gnu.org/licenses">http://www.gnu.org/licenses</a></span>.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X8354C98179CDB193">1 <span class="Heading">Maintenance Issues for the <strong class="pkg">GAP</strong> Character Table Library</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7ECA800587320C2C">1.1 <span class="Heading">Disproving Possible Character Tables (November 2006)</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X795DCCEA7F4D187A">1.1-1 <span class="Heading">A Perfect Pseudo Character Table (November 2006)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X80F0B4E07B0B2277">1.1-2 <span class="Heading">An Error in the Character Table of <span class="SimpleMath">\(E_6(2)\)</span> (March 2016)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D7982CD87413F76">1.1-3 <span class="Heading">An Error in a Power Map of the Character Table of <span class="SimpleMath">\(2.F_4(2).2\)</span> (November 2015)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X836E4B6184F32EF5">1.1-4 <span class="Heading">A Character Table with a Wrong Name (May 2017)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8159D79C7F071B33">1.2 <span class="Heading">Some finite factor groups of perfect space groups (February 2014)</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8710D4947AEB366F">1.2-1 <span class="Heading">Constructing the space groups in question</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X84E7FE70843422B0">1.2-2 <span class="Heading">Constructing the factor groups in question</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X79109A20873E76DA">1.2-3 <span class="Heading">Examples with point group <span class="SimpleMath">\(A_5\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X83523D1E792F9E01">1.2-4 <span class="Heading">Examples with point group <span class="SimpleMath">\(L_3(2)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7A01A9BC846BE39A">1.2-5 <span class="Heading">Example with point group SL<span class="SimpleMath">\(_2(7)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D3100B58093F37D">1.2-6 <span class="Heading">Example with point group <span class="SimpleMath">\(2^3.L_3(2)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X80800F3B7D6EF06C">1.2-7 <span class="Heading">Examples with point group <span class="SimpleMath">\(A_6\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D43452C79B0EAE1">1.2-8 <span class="Heading">Examples with point group <span class="SimpleMath">\(L_2(8)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8575CE147A9819BF">1.2-9 <span class="Heading">Example with point group <span class="SimpleMath">\(M_{11}\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7C0201B77DA1682A">1.2-10 <span class="Heading">Example with point group <span class="SimpleMath">\(U_3(3)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X85D9C329792E58F3">1.2-11 <span class="Heading">Examples with point group <span class="SimpleMath">\(U_4(2)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8635EE0B78A66120">1.2-12 <span class="Heading">A remark on one of the example groups</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8448022280E82C52">1.3 <span class="Heading">Generality problems (December 2004/October 2015)</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7D1A66C3844D09B1">1.3-1 <span class="Heading">Listing possible generality problems</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X80EB5D827A78975A">1.3-2 <span class="Heading">A generality problem concerning the group <span class="SimpleMath">\(J_3\)</span> (April 2015)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X82C37532783168AA">1.3-3 <span class="Heading">A generality problem concerning the group <span class="SimpleMath">\(HN\)</span> (August 2022)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7D8C6D1883C9CECA">1.4 <span class="Heading">Brauer Tables that can be derived from Known Tables</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7DF018B77E722CA7">1.4-1 <span class="Heading">Brauer Tables via Construction Information</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X795419A287BD228E">1.4-2 <span class="Heading">Liftable Brauer Characters (May 2017)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X864EFF897A854F89">1.5 <span class="Heading">Information about certain subgroups of the Monster group</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X82C7A03684DD7C6E">1.5-1 <span class="Heading">The Monster group does not contain subgroups of the type <span class="SimpleMath">\(2.U_4(2)\)</span> (August 2023)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X87EC0C48866D1BDE">1.5-2 <span class="Heading">Perfect central extensions of <span class="SimpleMath">\(L_3(4)\)</span> (August 2023)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7F605CA28441687F">1.5-3 <span class="Heading">The character table of <span class="SimpleMath">\((2 \times O_8^+(3)).S_4 \leq 2.B\)</span> (October 2023)</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X7B77FD307F0DE563">2 <span class="Heading">Using Table Automorphisms for Constructing Character Tables in <strong class="pkg">GAP</strong></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X8389AD927B74BA4A">2.1 <span class="Heading">Overview</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7B6AEBDF7B857E2E">2.2 <span class="Heading">Theoretical Background</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X78EBF9BA7A34A9C2">2.2-1 <span class="Heading">Character Table Automorphisms</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X832525DE7AB34F16">2.2-2 <span class="Heading">Permutation Equivalence of Character Tables</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7906869F7F190E76">2.2-3 <span class="Heading">Class Fusions</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X80C37276851D5E39">2.2-4 <span class="Heading">Constructing Character Tables of Certain Isoclinic Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7AEFFEEC84511FD0">2.2-5 <span class="Heading">Character Tables of Isoclinic Groups of the Structure <span class="SimpleMath">\(p.G.p\)</span>
(October 2016)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X78F41D2A78E70BEE">2.2-6 <span class="Heading">Isoclinic Double Covers of Almost Simple Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X834B42A07E98FBC6">2.2-7 <span class="Heading">Characters of Normal Subgroups</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X787F430E7FDB8765">2.3 <span class="Heading">The Constructions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X82E75B6880EC9E6C">2.3-1 <span class="Heading">Character Tables of Groups of the Structure <span class="SimpleMath">\(M.G.A\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7CCABDDE864E6300">2.3-2 <span class="Heading">Character Tables of Groups of the Structure <span class="SimpleMath">\(G.S_3\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7D3EF3BC83BE05CF">2.3-3 <span class="Heading">Character Tables of Groups of the Structure <span class="SimpleMath">\(G.2^2\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X81464C4B8178C85A">2.3-4 <span class="Heading">Character Tables of Groups of the Structure <span class="SimpleMath">\(2^2.G\)</span>
(August 2005)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X86CF6A607B0827EE">2.3-5 <span class="Heading"><span class="SimpleMath">\(p\)</span>-Modular Tables of Extensions by <span class="SimpleMath">\(p\)</span>-singular Automorphisms</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X788591D78451C024">2.3-6 <span class="Heading">Character Tables of Subdirect Products of Index Two (July 2007)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X817D2134829FA8FA">2.4 <span class="Heading">Examples for the Type <span class="SimpleMath">\(M.G.A\)</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7F2DBAB48437052C">2.4-1 <span class="Heading">Character Tables of Dihedral Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7925DBFA7C5986B5">2.4-2 <span class="Heading">An <span class="SimpleMath">\(M.G.A\)</span> Type Example with <span class="SimpleMath">\(M\)</span> noncentral in <span class="SimpleMath">\(M.G\)</span> (May 2004)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7ED45AB379093A70">2.4-3 <span class="Heading"><strong class="pkg">Atlas</strong> Tables of the Type <span class="SimpleMath">\(M.G.A\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7A236EDE7A7A28F9">2.4-4 <span class="Heading">More <strong class="pkg">Atlas</strong> Tables of the Type <span class="SimpleMath">\(M.G.A\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X794EC2FD7F69B4E6">2.4-5 <span class="Heading">The Character Tables of <span class="SimpleMath">\(4_2.L_3(4).2_3\)</span> and <span class="SimpleMath">\(12_2.L_3(4).2_3\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7E3E748E85AEDDB3">2.4-6 <span class="Heading">The Character Tables of <span class="SimpleMath">\(12_1.U_4(3).2_2'\) and
<span class="SimpleMath">\(12_2.U_4(3).2_3'\) (December 2015)
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8379003582D06130">2.4-7 <span class="Heading">Groups of the Structures <span class="SimpleMath">\(3.U_3(8).3_1\)</span> and <span class="SimpleMath">\(3.U_3(8).6\)</span>
(February 2017)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7B46C77B850D3B4D">2.4-8 <span class="Heading">The Character Table of <span class="SimpleMath">\((2^2 \times F_4(2)):2 < B\)</span>
(March 2003)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8254AA4A843F99BE">2.4-9 <span class="Heading">The Character Table of <span class="SimpleMath">\(2.(S_3 \times Fi_{22}.2) < 2.B\)</span> (March 2003)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7AF125168239D208">2.4-10 <span class="Heading">The Character Table of <span class="SimpleMath">\((2 \times 2.Fi_{22}):2 < Fi_{24}\)</span> (November 2008)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X79C93F7D87D9CF1D">2.4-11 <span class="Heading">The Character Table of <span class="SimpleMath">\(S_3 \times 2.U_4(3).2_2 \leq 2.Fi_{22}\)</span> (September 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X83724BCE86FCD77B">2.4-12 <span class="Heading">The Character Table of <span class="SimpleMath">\(4.HS.2 \leq HN.2\)</span> (May 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7E9A88DA7CBF6426">2.4-13 <span class="Heading">The Character Tables of <span class="SimpleMath">\(4.A_6.2_3\)</span>, <span class="SimpleMath">\(12.A_6.2_3\)</span>,
and <span class="SimpleMath">\(4.L_2(25).2_3\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7BD79BA37C3E729B">2.4-14 <span class="Heading">The Character Table of <span class="SimpleMath">\(4.L_2(49).2_3\)</span> (December 2020)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X817A961487D2DFD1">2.4-15 <span class="Heading">The Character Table of <span class="SimpleMath">\(4.L_2(81).2_3\)</span> (December 2020)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7AF324AF7A54798F">2.4-16 <span class="Heading">The Character Table of <span class="SimpleMath">\(9.U_3(8).3_3\)</span> (March 2017)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7E0C603880157C4E">2.4-17 <span class="Heading">Pseudo Character Tables of the Type <span class="SimpleMath">\(M.G.A\)</span> (May 2004)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X844185EF7A8F2A99">2.4-18 <span class="Heading">Some Extra-ordinary <span class="SimpleMath">\(p\)</span>-Modular Tables of the Type <span class="SimpleMath">\(M.G.A\)</span>
(September 2005)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7F50C782840F06E4">2.5 <span class="Heading">Examples for the Type <span class="SimpleMath">\(G.S_3\)</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7F0DC29F874AA09F">2.5-1 <span class="Heading">Small Examples</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X80F9BC057980A9E9">2.5-2 <span class="Heading"><strong class="pkg">Atlas</strong> Tables of the Type <span class="SimpleMath">\(G.S_3\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7EA489E07D7C7D86">2.6 <span class="Heading">Examples for the Type <span class="SimpleMath">\(G.2^2\)</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8054FDE679053B1C">2.6-1 <span class="Heading">The Character Table of <span class="SimpleMath">\(A_6.2^2\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7FEC3AB081487AF2">2.6-2 <span class="Heading"><strong class="pkg">Atlas</strong> Tables of the Type <span class="SimpleMath">\(G.2^2\)</span> – Easy Cases</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X869B65D3863EDEC3">2.6-3 <span class="Heading">The Character Table of <span class="SimpleMath">\(S_4(9).2^2\)</span> (September 2011)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7B38006380618543">2.6-4 <span class="Heading">The Character Tables of Groups of the Type <span class="SimpleMath">\(2.L_3(4).2^2\)</span>
(June 2010)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X79818ABD7E972370">2.6-5 <span class="Heading">The Character Tables of Groups of the Type <span class="SimpleMath">\(6.L_3(4).2^2\)</span>
(October 2011)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X878889308653435F">2.6-6 <span class="Heading">The Character Tables of Groups of the Type <span class="SimpleMath">\(2.U_4(3).2^2\)</span>
(February 2012)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7DC42AE57E9EED4D">2.6-7 <span class="Heading">The Character Tables of Groups of the Type <span class="SimpleMath">\(4_1.L_3(4).2^2\)</span>
(October 2011)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7E9AF180869B4786">2.6-8 <span class="Heading">The Character Tables of Groups of the Type <span class="SimpleMath">\(4_2.L_3(4).2^2\)</span>
(October 2011)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7EAF9CD07E536120">2.6-9 <span class="Heading">The Character Table of Aut<span class="SimpleMath">\((L_2(81))\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X78AED04685EDCC19">2.6-10 <span class="Heading">The Character Table of <span class="SimpleMath">\(O_8^+(3).2^2_{111}\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X845BAA2A7FD768B0">2.7 <span class="Heading">Examples for the Type <span class="SimpleMath">\(2^2.G\)</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X87EEBDB987249117">2.7-1 <span class="Heading">The Character Table of <span class="SimpleMath">\(2^2.Sz(8)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X83652A0282A64D14">2.7-2 <span class="Heading"><strong class="pkg">Atlas</strong> Tables of the Type <span class="SimpleMath">\(2^2.G\)</span> (September 2005)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7F63DDF77870F967">2.7-3 <span class="Heading">The Character Table of <span class="SimpleMath">\(2^2.O_8^+(3)\)</span> (March 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X86A1607787DE6BB9">2.7-4 <span class="Heading">The Character Table of the Schur Cover of <span class="SimpleMath">\(L_3(4)\)</span>
(September 2005)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X8711DBB083655A25">2.8 <span class="Heading">Examples of Extensions by <span class="SimpleMath">\(p\)</span>-singular Automorphisms</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X81C08739850E4AAE">2.8-1 <span class="Heading">Some <span class="SimpleMath">\(p\)</span>-Modular Tables of Groups of the Type <span class="SimpleMath">\(M.G.A\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7FED618F83ACB7C2">2.8-2 <span class="Heading">Some <span class="SimpleMath">\(p\)</span>-Modular Tables of Groups of the Type <span class="SimpleMath">\(G.S_3\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7EEF6A7F8683177A">2.8-3 <span class="Heading"><span class="SimpleMath">\(2\)</span>-Modular Tables of Groups of the Type <span class="SimpleMath">\(G.2^2\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X875F8DD77C0997FA">2.8-4 <span class="Heading">The <span class="SimpleMath">\(3\)</span>-Modular Table of <span class="SimpleMath">\(U_3(8).3^2\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7A4D6044865E516B">2.9 <span class="Heading">Examples of Subdirect Products of Index Two</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X850FF694801700CF">2.9-1 <span class="Heading">Certain Dihedral Groups as Subdirect Products of Index Two</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X80C5D6FA83D7E2CF">2.9-2 <span class="Heading">The Character Table of <span class="SimpleMath">\((D_{10} \times HN).2 < M\)</span> (June 2008)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X85EECFD47EC252A2">2.9-3 <span class="Heading">A Counterexample (August 2015)</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap3_mj.html#X7A80D5ED7D6E57B7">3 <span class="Heading">Constructing Character Tables of Central Extensions in <strong class="pkg">GAP</strong></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X87B17873861E2F64">3.1 <span class="Heading">Coprime Central Extensions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X85CB2671851D1206">3.1-1 <span class="Heading">The Character Table Head</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7D8F6E5D7D632046">3.1-2 <span class="Heading">The Irreducible Characters</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X867D16E07D36560F">3.1-3 <span class="Heading">Ordering of Conjugacy Classes</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X813B9F5180A45077">3.1-4 <span class="Heading">Compatibility with Smaller Factor Groups</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7A489A5D79DA9E5C">3.2 <span class="Heading">Examples</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X861B5C3F7B1F6AB7">3.2-1 <span class="Heading">Central Extensions of Simple <strong class="pkg">Atlas</strong> Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X799ADD5487613BA2">3.2-2 <span class="Heading">Central Extensions of Other <strong class="pkg">Atlas</strong> Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X861F558380FE4812">3.2-3 <span class="Heading">Compatible Central Extensions of Maximal Subgroups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7C73944579D6EE73">3.2-4 <span class="Heading">The <code class="code">2B</code> Centralizer in <span class="SimpleMath">\(3.Fi_{24}'\) (January 2004)
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X7D5919C182B1A462">4 <span class="Heading"><strong class="pkg">GAP</strong> Computations Concerning Hamiltonian Cycles in the Generating Graphs of Finite Groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X8389AD927B74BA4A">4.1 <span class="Heading">Overview</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7B6AEBDF7B857E2E">4.2 <span class="Heading">Theoretical Background</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7AD3962D7AE4ADFB">4.2-1 <span class="Heading">Character-Theoretic Lower Bounds for Vertex Degrees</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X825776BA8687E475">4.2-2 <span class="Heading">Checking the Criteria</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7B56BE5384BAD54E">4.3 <span class="Heading"><strong class="pkg">GAP</strong> Functions for the Computations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X802B2ED2802334B0">4.3-1 <span class="Heading">Computing Vertex Degrees from the Group</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87FE2DDD7F086D2F">4.3-2 <span class="Heading">Computing Lower Bounds for Vertex Degrees</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8677A8B1788ACD2C">4.3-3 <span class="Heading">Evaluating the (Lower Bounds for the) Vertex Degrees</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X7A221012861440E2">4.4 <span class="Heading">Character-Theoretic Computations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X86CE51E180A3D4ED">4.4-1 <span class="Heading">Sporadic Simple Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X867D338F7F453092">4.4-2 <span class="Heading">The Monster</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7DC6DFCC83502CC3">4.4-3 <span class="Heading">Nonsimple Automorphism Groups of Sporadic Simple Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8130C9CB7A33140F">4.4-4 <span class="Heading">Alternating and Symmetric Groups <span class="SimpleMath">\(A_n\)</span>, <span class="SimpleMath">\(S_n\)</span>,
for <span class="SimpleMath">\(5 \leq n \leq 13\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X83DACCF07EF62FAE">4.5 <span class="Heading">Computations With Groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7B9ADC91802EE09F">4.5-1 <span class="Heading">Nonabelian Simple Groups of Order up to <span class="SimpleMath">\(10^7\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8033892B7FD6E62B">4.5-2 <span class="Heading">Nonsimple Groups with Nonsolvable Socle of Order at most <span class="SimpleMath">\(10^6\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X84E62545802FAB30">4.6 <span class="Heading">The Groups <span class="SimpleMath">\(PSL(2,q)\)</span></span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap5_mj.html#X8703EFEE81DDE3DD">5 <span class="Heading"><strong class="pkg">GAP</strong> Computations with <span class="SimpleMath">\(O_8^+(5).S_3\)</span> and <span class="SimpleMath">\(O_8^+(2).S_3\)</span></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X8389AD927B74BA4A">5.1 <span class="Heading">Overview</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X85FF559084C08F0F">5.2 <span class="Heading">Constructing Representations of <span class="SimpleMath">\(M.2\)</span> and <span class="SimpleMath">\(S.2\)</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7FEE53AB845B9327">5.2-1 <span class="Heading">A Matrix Representation of the Weyl Group of Type <span class="SimpleMath">\(E_8\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7C8AA7747F160F8A">5.2-2 <span class="Heading">Embedding the Weyl group of Type <span class="SimpleMath">\(E_8\)</span> into GO<span class="SimpleMath">\({}^+(8,5)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X83E3E79F8724C365">5.2-3 <span class="Heading">Compatible Generators of <span class="SimpleMath">\(M\)</span>, <span class="SimpleMath">\(M.2\)</span>, <span class="SimpleMath">\(S\)</span>, and <span class="SimpleMath">\(S.2\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X83F897DD7C48511C">5.3 <span class="Heading">Constructing Representations of <span class="SimpleMath">\(M.3\)</span> and <span class="SimpleMath">\(S.3\)</span></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7B7561D0855EC4F1">5.3-1 <span class="Heading">The Action of <span class="SimpleMath">\(M.3\)</span> on <span class="SimpleMath">\(M\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X8246803779EB8FEE">5.3-2 <span class="Heading">The Action of <span class="SimpleMath">\(S.3\)</span> on <span class="SimpleMath">\(S\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X816AFA187E95C018">5.4 <span class="Heading">Constructing Compatible Generators of <span class="SimpleMath">\(H\)</span> and <span class="SimpleMath">\(G\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X83F0387D789709D1">5.5 <span class="Heading">Application: Regular Orbits of <span class="SimpleMath">\(H\)</span> on <span class="SimpleMath">\(G/H\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7F0C266082BE1578">5.6 <span class="Heading">Appendix: The Permutation Character <span class="SimpleMath">\((1_H^G)_H\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7F3A630780F8E262">5.7 <span class="Heading">Appendix: The Data File</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap6_mj.html#X7EF73AA88384B5F3">6 <span class="Heading">Solvable Subgroups of Maximal Order in Sporadic Simple Groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7F817DC57A69CF0D">6.1 <span class="Heading">The Result</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X876F77197B2FB84A">6.2 <span class="Heading">The Approach</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X792957AB7B24C5E0">6.2-1 <span class="Heading">Use the Table of Marks</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7B39A4467A1CCF8A">6.2-2 <span class="Heading">Use Information from the Character Table Library</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X834298A87BF43AAF">6.3 <span class="Heading">Cases where the Table of Marks is available in <strong class="pkg">GAP</strong></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X85559C0F7AA73E48">6.4 <span class="Heading">Cases where the Table of Marks is not available in <strong class="pkg">GAP</strong></span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7E393459822E78B5">6.4-1 <span class="Heading"><span class="SimpleMath">\(G = Ru\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7AFF09337CCB7745">6.4-2 <span class="Heading"><span class="SimpleMath">\(G = Suz\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7969AE067D3862A3">6.4-3 <span class="Heading"><span class="SimpleMath">\(G = ON\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X84921B85845EDA31">6.4-4 <span class="Heading"><span class="SimpleMath">\(G = Co_2\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7D777A0D82BE8498">6.4-5 <span class="Heading"><span class="SimpleMath">\(G = Fi_{22}\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7D9DB76A861A6F62">6.4-6 <span class="Heading"><span class="SimpleMath">\(G = HN\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X83E6436678AF562C">6.4-7 <span class="Heading"><span class="SimpleMath">\(G = Ly\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7D6CF8EC812EF6FB">6.4-8 <span class="Heading"><span class="SimpleMath">\(G = Th\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7A07090483C935DC">6.4-9 <span class="Heading"><span class="SimpleMath">\(G = Fi_{23}\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7D028E9E7CB62A4F">6.4-10 <span class="Heading"><span class="SimpleMath">\(G = Co_1\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X84208AB781344A9D">6.4-11 <span class="Heading"><span class="SimpleMath">\(G = J_4\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7BC589718203F125">6.4-12 <span class="Heading"><span class="SimpleMath">\(G = Fi_{24}^{\prime}\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X7EDF990985573EB6">6.4-13 <span class="Heading"><span class="SimpleMath">\(G = B\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap6_mj.html#X87D468D07D7237CB">6.4-14 <span class="Heading"><span class="SimpleMath">\(G = M\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6_mj.html#X7CD8E04C7F32AD56">6.5 <span class="Heading">Proof of the Corollary</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap7_mj.html#X8102827B85FE3BCA">7 <span class="Heading">Large Nilpotent Subgroups of Sporadic Simple Groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X7F817DC57A69CF0D">7.1 <span class="Heading">The Result</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X787B841383A16711">7.2 <span class="Heading">The Proof</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap7_mj.html#X798EACC07F6C36D9">7.3 <span class="Heading">Alternative: Use <strong class="pkg">GAP</strong>'s Tables of Marks
</span>
</div>
</div>
<div class="ContChap"><a href="chap8_mj.html#X7A7EEBE9858333E1">8 <span class="Heading">Permutation Characters in <strong class="pkg">GAP</strong></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X86A1325B82E5AECD">8.1 <span class="Heading">Some Computations with <span class="SimpleMath">\(M_{24}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X79C9051F805851DB">8.2 <span class="Heading">All Possible Permutation Characters of <span class="SimpleMath">\(M_{11}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X81A5FC968782CFC3">8.3 <span class="Heading">The Action of <span class="SimpleMath">\(U_6(2)\)</span> on the Cosets of <span class="SimpleMath">\(M_{22}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X7EE1811C8496C428">8.4 <span class="Heading">Degree <span class="SimpleMath">\(20\,736\)</span> Permutation Characters of <span class="SimpleMath">\(U_6(2)\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X7DC6A6E785A347C8">8.5 <span class="Heading">Degree <span class="SimpleMath">\(57\,572\,775\)</span> Permutation Characters of <span class="SimpleMath">\(O_8^+(3)\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X792D2C2380591D8D">8.6 <span class="Heading">The Action of <span class="SimpleMath">\(O_7(3).2\)</span> on the Cosets of <span class="SimpleMath">\(2^7.S_7\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X875B361C8512939F">8.7 <span class="Heading">The Action of <span class="SimpleMath">\(O_8^+(3).2_1\)</span> on the Cosets of <span class="SimpleMath">\(2^7.A_8\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X7B1DFAF98182CFF4">8.8 <span class="Heading">The Action of <span class="SimpleMath">\(S_4(4).4\)</span> on the Cosets of <span class="SimpleMath">\(5^2.[2^5]\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X7F04F0C684AA8B30">8.9 <span class="Heading">The Action of <span class="SimpleMath">\(Co_1\)</span> on the Cosets of Involution Centralizers</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X8230719D8538384B">8.10 <span class="Heading">The Multiplicity Free Permutation Characters of <span class="SimpleMath">\(G_2(3)\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X7E3E326C7CB0E2CD">8.11 <span class="Heading">Degree <span class="SimpleMath">\(11\,200\)</span> Permutation Characters of <span class="SimpleMath">\(O_8^+(2)\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X7D8572E68194CBB9">8.12 <span class="Heading">A Proof of Nonexistence of a Certain Subgroup</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X8068E9DA7CD03BF2">8.13 <span class="Heading">A Permutation Character of the Lyons group</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X87D6C1A67CC7EE0A">8.14 <span class="Heading">Identifying two subgroups of Aut<span class="SimpleMath">\((U_3(5))\)</span> (October 2001)</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X793669787CF73A55">8.15 <span class="Heading">A Permutation Character of Aut<span class="SimpleMath">\((O_8^+(2))\)</span> (October 2001)</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X8337F3C682B6BE63">8.16 <span class="Heading">Four Primitive Permutation Characters of the Monster Group</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X78A8A1248336DD26">8.16-1 <span class="Heading">The Subgroup <span class="SimpleMath">\(2^2.2^{11}.2^{22}.(S_3 \times M_{24})\)</span>
(June 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X79E9247182B20474">8.16-2 <span class="Heading">The Subgroup <span class="SimpleMath">\(2^3.2^6.2^{12}.2^{18}.(L_3(2) \times 3.S_6)\)</span>
(September 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X7BC36C597E542DEE">8.16-3 <span class="Heading">The Subgroup <span class="SimpleMath">\(2^5.2^{10}.2^{20}.(S_3 \times L_5(2))\)</span>
(October 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X7F2ABD3E7AFF5F6E">8.16-4 <span class="Heading">The Subgroup <span class="SimpleMath">\(2^{{10+16}}.O_{10}^+(2)\)</span> (November 2009)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X87D11B097D95D027">8.17 <span class="Heading">A permutation character of the Baby Monster (June 2012)</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X86827FA97D27F3A2">8.18 <span class="Heading">A permutation character of <span class="SimpleMath">\(2.B\)</span> (October 2017)</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap8_mj.html#X849F0EA6807C9B19">8.19 <span class="Heading">Generation of sporadic simple groups by <span class="SimpleMath">\(\pi\)</span>- and <span class="SimpleMath">\(\pi'\)-subgroups (December 2021)
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap8_mj.html#X839272078243F4DB">8.19-1 <span class="Heading">Special Arguments for the Monster Group that are no longer needed</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap9_mj.html#X7A03A83E87FB1189">9 <span class="Heading">Ambiguous Class Fusions in the <strong class="pkg">GAP</strong> Character Table Library</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X784492877DB04FE9">9.1 <span class="Heading">Some <strong class="pkg">GAP</strong> Utilities</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X7EA839057D3AD3B4">9.2 <span class="Heading">Fusions Determined by Factorization through Intermediate Subgroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X78DCEEFD85FF1EE2">9.2-1 <span class="Heading"><span class="SimpleMath">\(Co_3N5 \rightarrow Co_3\)</span> (September 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X86BCEA907EC4C833">9.2-2 <span class="Heading"><span class="SimpleMath">\(31:15 \rightarrow B\)</span> (March 2003)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7C719F527831F35A">9.2-3 <span class="Heading"><span class="SimpleMath">\(SuzN3 \rightarrow Suz\)</span> (September 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X828879F481EF30DD">9.2-4 <span class="Heading"><span class="SimpleMath">\(F_{{3+}}N5 \rightarrow F_{{3+}}\)</span> (March 2002)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X7981579278F81AC6">9.3 <span class="Heading">Fusions Determined Using Commutative Diagrams Involving Smaller
Subgroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7F5186E28201B027">9.3-1 <span class="Heading"><span class="SimpleMath">\(BN7 \rightarrow B\)</span> (March 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X79710B137B5BB1B8">9.3-2 <span class="Heading"><span class="SimpleMath">\((A_4 \times O_8^+(2).3).2 \rightarrow Fi_{24}^{\prime}\)</span> (November 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X85822C647B29117B">9.3-3 <span class="Heading"><span class="SimpleMath">\(A_6 \times L_2(8).3 \rightarrow Fi_{24}^{\prime}\)</span> (November 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X81A607758682D9A9">9.3-4 <span class="Heading"><span class="SimpleMath">\((3^2:D_8 \times U_4(3).2^2).2 \rightarrow B\)</span> (June 2007)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7962DD4387D63675">9.3-5 <span class="Heading"><span class="SimpleMath">\(7^{1+4}:(3 \times 2.S_7) \rightarrow M\)</span> (May 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X860B6C30812DE3FC">9.3-6 <span class="Heading"><span class="SimpleMath">\(3^7.O_7(3):2 \rightarrow Fi_{24}\)</span> (November 2010)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7C3AC42F8342EE2E">9.3-7 <span class="Heading"><span class="SimpleMath">\({}^2E_6(2)N3C \rightarrow {}^2E_6(2)\)</span> (January 2019)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X84F966E2824F5D52">9.4 <span class="Heading">Fusions Determined Using Commutative Diagrams Involving Factor
Groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7F2B104686509CAA">9.4-1 <span class="Heading"><span class="SimpleMath">\(3.A_7 \rightarrow 3.Suz\)</span> (December 2010)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X82FB71647D37F4FD">9.4-2 <span class="Heading"><span class="SimpleMath">\(S_6 \rightarrow U_4(2)\)</span> (September 2011)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X7CFBC41B818A318C">9.5 <span class="Heading">Fusions Determined Using Commutative Diagrams Involving
Automorphic Extensions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7E91F8707BA93081">9.5-1 <span class="Heading"><span class="SimpleMath">\(U_3(8).3_1 \rightarrow {}^2E_6(2)\)</span> (December 2010)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X81B37EF378E89E00">9.5-2 <span class="Heading"><span class="SimpleMath">\(L_3(4).2_1 \rightarrow U_6(2)\)</span> (December 2010)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X85E2A6F480026C95">9.6 <span class="Heading">Conditions Imposed by Brauer Tables</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7ACC7F588213D5D5">9.6-1 <span class="Heading"><span class="SimpleMath">\(L_2(16).4 \rightarrow J_3.2\)</span> (January 2004)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7ACB86CB82ED49D1">9.6-2 <span class="Heading"><span class="SimpleMath">\(L_2(17) \rightarrow S_8(2)\)</span> (July 2004)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7DED4C437D479226">9.6-3 <span class="Heading"><span class="SimpleMath">\(L_2(19) \rightarrow J_3\)</span> (April 2003)</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap9_mj.html#X8225D9FA80A7D20F">9.7 <span class="Heading">Fusions Determined by Information about the Groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7AE2962E82B4C814">9.7-1 <span class="Heading"><span class="SimpleMath">\(U_3(3).2 \rightarrow Fi_{24}^{\prime}\)</span> (November 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X83061094871EE241">9.7-2 <span class="Heading"><span class="SimpleMath">\(L_2(13).2 \rightarrow Fi_{24}^{\prime}\)</span> (September 2002)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7E9C203C7C4D709D">9.7-3 <span class="Heading"><span class="SimpleMath">\(M_{11} \rightarrow B\)</span> (April 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X85821D748716DC7E">9.7-4 <span class="Heading"><span class="SimpleMath">\(L_2(11):2 \rightarrow B\)</span> (April 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X828D81487F57D612">9.7-5 <span class="Heading"><span class="SimpleMath">\(L_3(3) \rightarrow B\)</span> (April 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7B4E13337D66020F">9.7-6 <span class="Heading"><span class="SimpleMath">\(L_2(17).2 \rightarrow B\)</span> (March 2004)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X8528432A84851F7B">9.7-7 <span class="Heading"><span class="SimpleMath">\(L_2(49).2_3 \rightarrow B\)</span> (June 2006)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7EAD52AA7A28D956">9.7-8 <span class="Heading"><span class="SimpleMath">\(2^3.L_3(2) \rightarrow G_2(5)\)</span> (January 2004)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X79617107849A6CEA">9.7-9 <span class="Heading"><span class="SimpleMath">\(5^{{1+4}}.2^{{1+4}}.A_5.4 \rightarrow B\)</span> (April 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X85C48EEB7B711C09">9.7-10 <span class="Heading">The fusion from the character table of <span class="SimpleMath">\(7^2:2L_2(7).2\)</span>
into the table of marks (January 2004)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7B1C689C7EFD07CB">9.7-11 <span class="Heading"><span class="SimpleMath">\(3 \times U_4(2) \rightarrow 3_1.U_4(3)\)</span> (March 2010)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7A94F78C792122D5">9.7-12 <span class="Heading"><span class="SimpleMath">\(2.3^4.2^3.S_4 \rightarrow 2.A12\)</span> (September 2011)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X7E2AF30C7E8F89F9">9.7-13 <span class="Heading"><span class="SimpleMath">\(127:7 \rightarrow L_7(2)\)</span> (January 2012)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X80051B297DF244CF">9.7-14 <span class="Heading"><span class="SimpleMath">\(L_2(59) \rightarrow M\)</span> (May 2009) – Do not use this!</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X8409DA2E83A41ABE">9.7-15 <span class="Heading"><span class="SimpleMath">\(L_2(71) \rightarrow M\)</span> (May 2009)</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap9_mj.html#X78B3B1BE7A2CA4D1">9.7-16 <span class="Heading"><span class="SimpleMath">\(L_2(41) \rightarrow M\)</span> (April 2012)</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap10_mj.html#X831E9D0A7A2DBC72">10 <span class="Heading"><strong class="pkg">GAP</strong> computations needed in the proof of
<a href="chapBib_mj.html#biBDNT">[DNT13, Theorem 6.1 (ii)]</a></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10_mj.html#X82BDD020860C6E95">10.1 <span class="Heading"><span class="SimpleMath">\(G/N \cong Sz(8)\)</span> and <span class="SimpleMath">\(|N| = 2^{12}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10_mj.html#X7C01350E8217B0B1">10.2 <span class="Heading"><span class="SimpleMath">\(G/N \cong M_{22}\)</span> and <span class="SimpleMath">\(|N| = 2^{10}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10_mj.html#X7E356703856DF22E">10.3 <span class="Heading"><span class="SimpleMath">\(G/N \cong J_2\)</span> and <span class="SimpleMath">\(|N| = 2^{12}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10_mj.html#X797E2EDB78F05F6E">10.4 <span class="Heading"><span class="SimpleMath">\(G/N \cong J_2\)</span> and <span class="SimpleMath">\(|N| = 5^{14}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10_mj.html#X828AECAE82B0CEB6">10.5 <span class="Heading"><span class="SimpleMath">\(G/N \cong J_2\)</span> and <span class="SimpleMath">\(|N| = 2^{28}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10_mj.html#X81AB173981E3EED7">10.6 <span class="Heading"><span class="SimpleMath">\(G/N \cong {}^3D_4(2)\)</span> and <span class="SimpleMath">\(|N| = 2^{26}\)</span></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap10_mj.html#X83B044547B96B7A5">10.7 <span class="Heading"><span class="SimpleMath">\(G/N \cong {}^3D_4(2)\)</span> and <span class="SimpleMath">\(|N| = 3^{25}\)</span></span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap11_mj.html#X7BE9906583D0FCEC">11 <span class="Heading"><strong class="pkg">GAP</strong> Computations Concerning Probabilistic Generation of Finite
Simple Groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11_mj.html#X8389AD927B74BA4A">11.1 <span class="Heading">Overview</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11_mj.html#X7B4649CF7B7CFAA1">11.2 <span class="Heading">Prerequisites</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X7B6AEBDF7B857E2E">11.2-1 <span class="Heading">Theoretical Background</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X79D7312484E78274">11.2-2 <span class="Heading">Computational Criteria</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11_mj.html#X7B56BE5384BAD54E">11.3 <span class="Heading"><strong class="pkg">GAP</strong> Functions for the Computations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X806328747D1D4ECC">11.3-1 <span class="Heading">General Utilities</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X7A221012861440E2">11.3-2 <span class="Heading">Character-Theoretic Computations</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X83DACCF07EF62FAE">11.3-3 <span class="Heading">Computations with Groups</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11_mj.html#X7A221012861440E2">11.4 <span class="Heading">Character-Theoretic Computations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X86CE51E180A3D4ED">11.4-1 <span class="Heading">Sporadic Simple Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X821778BC7D665AB4">11.4-2 <span class="Heading">No longer necessary computations for the Baby Monster and the Monster</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X84E9D10F80A74A53">11.4-3 <span class="Heading">Automorphism Groups of Sporadic Simple Groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X80DA58F187CDCF5F">11.4-4 <span class="Heading">Other Simple Groups – Easy Cases</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X7B1E26D586337487">11.4-5 <span class="Heading">Automorphism Groups of other Simple Groups – Easy Cases</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X78B856907ED13545">11.4-6 <span class="Heading"><span class="SimpleMath">\(O_8^-(3)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X84AB334886DCA746">11.4-7 <span class="Heading"><span class="SimpleMath">\(O_{10}^+(2)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X84E3E4837BB93977">11.4-8 <span class="Heading"><span class="SimpleMath">\(O_{10}^-(2)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X8307367E7C7C3BCE">11.4-9 <span class="Heading"><span class="SimpleMath">\(O_{12}^+(2)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X834FE1B58119A5FF">11.4-10 <span class="Heading"><span class="SimpleMath">\(O_{12}^-(2)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X7C5980A385C088FA">11.4-11 <span class="Heading"><span class="SimpleMath">\(S_6(4)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X829EDF7F7C0BCB8E">11.4-12 <span class="Heading"><span class="SimpleMath">\(\ast\)</span> <span class="SimpleMath">\(S_6(5)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X85162B297E4B67EB">11.4-13 <span class="Heading"><span class="SimpleMath">\(S_8(3)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X8495C2BF7B6EFFEF">11.4-14 <span class="Heading"><span class="SimpleMath">\(U_4(4)\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X7A3BB5AA83A2BDF3">11.4-15 <span class="Heading"><span class="SimpleMath">\(U_6(2)\)</span></span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap11_mj.html#X8237B8617D6F6027">11.5 <span class="Heading">Computations using Groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X815320787B601000">11.5-1 <span class="Heading"><span class="SimpleMath">\(A_{2m+1}\)</span>, <span class="SimpleMath">\(2 \leq m \leq 11\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X7B5321337B28100B">11.5-2 <span class="Heading"><span class="SimpleMath">\(A_5\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X82C3B4287B0C7BEE">11.5-3 <span class="Heading"><span class="SimpleMath">\(A_6\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X85B3C7217B105D4D">11.5-4 <span class="Heading"><span class="SimpleMath">\(A_7\)</span></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap11_mj.html#X84EA645A82E2BAFB">11.5-5 <span class="Heading"><span class="SimpleMath">\(L_d(q)\)</span></span></a>
</span>
--> --------------------

--> maximum size reached

--> --------------------

Messung V0.5
C=97 H=100 G=98

¤ Dauer der Verarbeitung: 0.24 Sekunden  (vorverarbeitet)  ¤

*© Formatika GbR, Deutschland




Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.