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<h1>corefreesub</h1>
<h2>A <strong class="pkg">GAP</strong> Package for calculating the core-free subgroups and their faithful transitive permutation representations</h2>
<p>
0.6</p>
<p>
11 March 2024
</p>
</div>
<p><b>
Claudio Alexandre Piedade
</b>
<br />Email: <span class="URL"><a href="mailto:claudio.piedade@fc.up.pt">claudio.piedade@fc.up.pt</a></span>
<br />Homepage: <span class="URL"><a href="https://www.fc.up.pt/pessoas/claudio.piedade/">https://www.fc.up.pt/pessoas/claudio.piedade/</a></span>
</p><p><b>
Manuel Delgado
</b>
<br />Email: <span class="URL"><a href="mailto:mdelgado@fc.up.pt">mdelgado@fc.up.pt</a></span>
<br />Homepage: <span class="URL"><a href="https://cmup.fc.up.pt/cmup/mdelgado/">https://cmup.fc.up.pt/cmup/mdelgado/</a></span>
</p>
<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p><strong class="pkg">corefreesub</strong> package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="http://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>
<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>The authors wish to thank all the comments, suggestions and issue reporting from users and developers of <strong class="pkg">GAP</strong>, both past and future. Both authors were partially supported by CMUP, member of LASI, which is financed by Portuguese national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the project with references UIDB/00144/2020 and UIDP/00144/2020.</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#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8360C04082558A12">1.1 <span class="Heading">Installation</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7862D3F37C5BBDEF">1.2 <span class="Heading">Testing your installation</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X78D8803A84DB6CE8">2 <span class="Heading">Obtaining Core-Free Subgroups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X79EF503F837B7702">2.1 <span class="Heading">Core-Free Subgroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2_mj.html#X7A9042C27F0BA85B">2.1-1 IsCoreFree</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2_mj.html#X7D0391668782765C">2.1-2 CoreFreeConjugacyClassesSubgroups</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2_mj.html#X821F9BD687383C1F">2.1-3 AllCoreFreeSubgroups</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X847B222E84342E88">2.2 <span class="Heading">Degrees of Core-Free subgroups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap2_mj.html#X844F04457C6EDC67">2.2-1 CoreFreeDegrees</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap3_mj.html#X857DD6BF86E302D0">3 <span class="Heading">Faithful Transitive Permutation Representations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X839E0E8B87479AB5">3.1 <span class="Heading">Obtaining Faithful Transitive Permutation Representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X80D610507B1029C9">3.1-1 FaithfulTransitivePermutationRepresentations</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X836069DB849BD28D">3.2 <span class="Heading">Faithful Transitive Permutation Representation of Minimal Degree</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X8746DBA2866336CC">3.2-1 MinimalFaithfulTransitivePermutationRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7B0EBFFA86B38A0F">3.2-2 MinimalFaithfulTransitivePermutationDegree</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X845EED7E826D411B">3.3 <span class="Heading">Faithful Transitive Permutation Representation of given Degree</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap3_mj.html#X7EC3C43C80AAD2CB">3.3-1 FaithfulTransitivePermutationRepresentationsOfDegree</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X85BCED3F87DE1C07">4 <span class="Heading">Drawing the Faithful Transitive Permutation Representation Graph</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X82F35AB4823114BD">4.1 <span class="Heading">Drawing functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4_mj.html#X785A165E8417A1D8">4.1-1 DotFTPRGraph</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4_mj.html#X8692BA897CFF04D4">4.1-2 DrawFTPRGraph</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4_mj.html#X7D0B40427CC8BFC5">4.1-3 TeXFTPRGraph</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap4_mj.html#X8721FD6E83582BA3">4.1-4 DrawTeXFTPRGraph</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X8099E0467907387C">4.2 <span class="Heading">Information Level of Drawing Functions</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
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