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<?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 >title >GAP (PERMUT) - 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.html" >Top</a> <a href="chap1.html" >1</a> <a href="chap2.html" >2</a> <a href="chap3.html" >3</a> <a href="chap4.html" >4</a> <a href="chap5.html" >5</a> <a href="chap6.html" >6</a> <a href="chap7.html" >7</a> <a href="chapBib.html" >Bib</a> <a href="chapInd.html" >Ind</a> </div >div class="chlinkprevnexttop" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >"mathjaxlink" class="pcenter" ><a href="chap0_mj.html" >[MathJax on]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >permut</h1 >div >br />Email: <span class="URL" ><a href="mailto:Adolfo.Ballester@uv.es" >Adolfo.Ballester@uv.es</a></span >br />Address : <br />Departament de Matemàtiques<br /> Universitat de València<br /> Dr. Moliner, 50<br /> 46100 Burjassot, València, Spain<br />br />Email: <span class="URL" ><a href="mailto:Enric.Cosme@uv.es" >Enric.Cosme@uv.es</a></span >br />Homepage: <span class="URL" ><a href="https://www.uv.es/coslloen " >https://www.uv.es/coslloen</a></span >br />Address : <br />Departament de Matemàtiques<br /> Universitat de València<br /> Dr. Moliner, 50<br /> 46100 Burjassot, València, Spain<br />br />Email: <span class="URL" ><a href="mailto:Ramon.Esteban@uv.es" >Ramon.Esteban@uv.es</a></span br />Homepage: <span class="URL" ><a href="https://www.uv.es/estebanr " >https://www.uv.es/estebanr</a></span >"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"contents" name="contents" ></a></h3>div class="ContChap" ><a href="chap1.html#X7A6D71137AE20820" >1 <span class="Heading" >Introduction to the <strong class="pkg" >PERMUT</strong > Package</span ></a>div >div class="ContChap" ><a href="chap2.html#X78FA2A627FAD92E6" >2 <span class="Heading" >Installation and Help of the <strong class="pkg" >PERMUT</strong > Package</span ></a>div >div class="ContChap" ><a href="chap3.html#X7B87CECD83EA77DF" >3 <span class="Heading" >Permutability of Subgroups in Finite Groups</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X834D77E17960C0B7" >3.1 <span class="Heading" >Permutability functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X862727A87C26B10B" >3.1-1 ArePermutableSubgroups</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap3.html#X875BEB9B7D0DBC9A" >3.2 <span class="Heading" >Embedding properties related to permutability</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X85CFBEBB83245E3A" >3.2-1 PermutMaxTries</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X80C15D427EC11A5F" >3.2-2 IsPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8244918D7D1C2703" >3.2-3 OneSubgroupNotPermutingWith</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X865C7F81823FFA10" >3.2-4 IsFPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X826D28757824F83E" >3.2-5 OneFSubgroupNotPermutingWith</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7BA6690983912C09" >3.2-6 IsSPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X83E103AF7C3DC9B7" >3.2-7 OneSylowSubgroupNotPermutingWith</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X86A62A52831BE00E" >3.2-8 IsSNPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X83D1BF5778D6790A" >3.2-9 OneSystemNormaliserNotPermutingWith</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7B2E052E7F9C4251" >3.2-10 IsConjugatePermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X809E1C8E8384ADE8" >3.2-11 OneConjugateSubgroupNotPermutingWith</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7AC58CFF87770C6C" >3.2-12 IsWeaklySPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X870923B4798E5097" >3.2-13 OneElementShowingNotWeaklySPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X85E85FBF78DAB08E" >3.2-14 IsWeaklyPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X8427C8DD78732D56" >3.2-15 OneElementShowingNotWeaklyPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X84BE89EF8140D2C0" >3.2-16 IsWeaklyNormal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X82C8AE027E578ACF" >3.2-17 OneElementShowingNotWeaklyNormal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X872EA72A7CEC3E65" >3.2-18 IsWithSubnormalizerCondition</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7FBEC9DD7C8AED52" >3.2-19 OneSubgroupInWhichSubnormalNotNormal</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X87CA542C7E1FEEF3" >3.2-20 IsWithSubpermutizerCondition</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X79648B4F8758E187" >3.2-21 OneSubgroupInWhichSubnormalNotPermutable</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X831F5B8787BB111F" >3.2-22 IsWithSSubpermutizerCondition</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap3.html#X7AC9002B7D5AB2DA" >3.2-23 OneSubgroupInWhichSubnormalNotSPermutable</a></span >div ></div >div >div class="ContChap" ><a href="chap4.html#X7E7EFDD1878F599D" >4 <span class="Heading" >T-groups, PT-groups, and PST-groups</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7ABC289380DB85BE" >4.1 <span class="Heading" >"One" functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7E15C5F778535A28" >4.1-1 OneSubnormalNonNormalSubgroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7F5EE21F85A8D14F" >4.1-2 OneSubnormalNonPermutableSubgroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7D7717657B9C7BEB" >4.1-3 OneSubnormalNonSPermutableSubgroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7878496C869CB90C" >4.1-4 OneSubnormalNonConjugatePermutableSubgroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7B23E3857CA178FE" >4.1-5 OneSubnormalNonSNPermutableSubgroup</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap4.html#X7B13DA0A800D8635" >4.2 <span class="Heading" >Group properties related to permutability</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7930E5AD817BE4B3" >4.2-1 IsTGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7CF2634F84EC572B" >4.2-2 IsPTGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7BB4D5A782FF5B0E" >4.2-3 IsPSTGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X8789176282320022" >4.2-4 IsCPTGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap4.html#X7B9EBEA07DBE246F" >4.2-5 IsPSNTGroup</a></span >div ></div >div >div class="ContChap" ><a href="chap5.html#X83F7986D84F33F6C" >5 <span class="Heading" >Local Functions in the <strong class="pkg" >PERMUT</strong > Package</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X7E8389FD7DE9769C" >5.1 <span class="Heading" >A Local Function for Supersolubility</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7B9F19A37F4A5B35" >5.1-1 IsPSupersolvable</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X7C4B2A9A7F2D7E0B" >5.2 <span class="Heading" >Local functions for T-groups, PT-groups, and PST-groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X780657F179FFB7EE" >5.2-1 IsCp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X82953B4878F88327" >5.2-2 IsXp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X8304885C78E4A584" >5.2-3 IsYp</a></span >div ></div >div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap5.html#X8540D4B679519F8B" >5.3 <span class="Heading" >Auxiliary Functions for T-groups, PT-groups, and PST-groups</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X8775CAFD80D3FC02" >5.3-1 IsAbCp</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7A6372D3871E8E55" >5.3-2 IsDedekindSylow</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X812C3A017F534CC0" >5.3-3 IwasawaTripleWithSubgroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X7E86B21086879C48" >5.3-4 IwasawaTriple</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap5.html#X8121A92F7EABEA0C" >5.3-5 IsIwasawaSylow</a></span >div ></div >div >div class="ContChap" ><a href="chap6.html#X82E82E45786E1B22" >6 <span class="Heading" >Totally and Mutually Permutable Products</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap6.html#X85291E9D86736F21" >6.1 <span class="Heading" >Functions for Mutually and Totally Permutable Products</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X876F4E0D7C796134" >6.1-1 AreMutuallyPermutableSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X80225ABC79C7875F" >6.1-2 OnePairShowingNotMutuallyPermutableSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7D58DFE57AA4573B" >6.1-3 AreTotallyPermutableSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7B51474D878ACD11" >6.1-4 OnePairShowingNotTotallyPermutableSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X823C6D68813B3AC8" >6.1-5 AreMutuallyFPermutableSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X83E0517A800AB839" >6.1-6 OnePairShowingNotMutuallyFPermutableSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7B9DA1C2834CA53D" >6.1-7 AreTotallyFPermutableSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap6.html#X7CD0B5737A25C1AD" >6.1-8 OnePairShowingNotTotallyFPermutableSubgroups</a></span >div ></div >div >div class="ContChap" ><a href="chap7.html#X840872AB823EB3DB" >7 <span class="Heading" >Other Functions in the <strong class="pkg" >PERMUT</strong > Package</span ></a>div class="ContSect" ><span class="tocline" ><span class="nocss" > </span ><a href="chap7.html#X86FA580F8055B274" >7.1 <span class="Heading" >Functions</span ></a>span >div class="ContSSBlock" >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X81EA23787BCD8633" >7.1-1 AllSubnormalSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X858C07DA815A2E9A" >7.1-2 PrimesDividingSize</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7B07AAD37F7CEDEB" >7.1-3 SylowSubgroups</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7E01D1C47814DA3C" >7.1-4 IsSCGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X798736C17DD23F8A" >7.1-5 IsSylowTowerGroup</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X81FCDD7C7A5D1658" >7.1-6 Permutizer</a></span >span class="ContSS" ><br /><span class="nocss" > </span ><a href="chap7.html#X7D47DF77826C1BE0" >7.1-7 AllGeneratorsCyclicPGroup</a></span >div ></div >div >div class="ContChap" ><a href="chapBib.html" ><span class="Heading" >References</span ></a></div >div class="ContChap" ><a href="chapInd.html" ><span class="Heading" >Index</span ></a></div >br />div >div class="chlinkprevnextbot" > <a href="chap0.html" >[Top of Book]</a> <a href="chap0.html#contents" >[Contents]</a> <a href="chap1.html" >[Next Chapter]</a> </div >div class="chlinkbot" ><span class="chlink1" >Goto Chapter: </span 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