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<h1>Repsn</h1>


<h2>Constructing representations of finite groups</h2>

<p>
    3.1.2</p>

<p>
    22 January 2024
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<p><b>
    Vahid Dabbaghian




  </b>
<br />Email: <span class="URL"><a href="mailto:vdabbagh@sfu.ca">vdabbagh@sfu.ca</a></span>
<br />Homepage: <span class="URL"><a href="https://www.sfu.ca/~vdabbagh">https://www.sfu.ca/~vdabbagh</a></span>
<br />Address: <br />Vahid Dabbaghian<br /> Department of Mathematics<br /> Simon Fraser University<br /> Burnaby, British Columbia<br /> V5A 1S6 Canada<br />
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<h3>Acknowledgements</h3>
<p>The first version of this package was obtained during my Ph.D. studies at Carleton University. I would like to express deep gratitude to my supervisor Professor John D. Dixon whose guidance and support were crucial for the successful completion of this project. I also thank Professor Charles Wright and referees for pointing out some important comments to improve <strong class="pkg">Repsn</strong>.</p>

<p>This documentation was prepared with the <strong class="pkg">GAPDoc</strong> package by Frank Lübeck and Max Neunhöffer.</p>

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<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>
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<div class="ContChap"><a href="chap2_mj.html#X8145828B844789C2">2 <span class="Heading">Irreducible Representations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X812E7C8E7FA7BE4E">2.1 <span class="Heading">Constructing Representations</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7A3ACAC179C15393">2.1-1 IrreducibleAffordingRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7CF2E8907C5C6D0D">2.1-2 IsAffordingRepresentation</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7EE113967DB4AB68">2.2 <span class="Heading">Induction</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X832316958253A958">2.2-1 InducedSubgroupRepresentation</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7B3BE908867CE4F9">2.3 <span class="Heading">Extension</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7950DD2D7B80E583">2.3-1 ExtendedRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X83536FA985B4E255">2.3-2 ExtendedRepresentationNormal</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X80C4BBFE7CDE7AA9">2.4 <span class="Heading">Character Subgroups</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X875FD501825F7AB8">2.4-1 CharacterSubgroupRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X79510CED811937D9">2.4-2 IsCharacterSubgroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X8408A559823FED05">2.4-3 AllCharacterPSubgroups</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X86388596828FDAFE">2.4-4 AllCharacterStandardSubgroups</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7A7B4ECC8722140C">2.4-5 AllCharacterSubgroups</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X8459AEDB7B73584F">2.5 <span class="Heading">Equivalent Representation</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X87C25B877C4952BA">2.5-1 EquivalentRepresentation</a></span>
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<div class="ContChap"><a href="chap3_mj.html#X826CC30186DBDB2B">3 <span class="Heading">Reducible Representations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7829A125780DD25D">3.1 <span class="Heading">Constituents of Representations</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7BBA5EC37C52A99D">3.1-1 ConstituentsOfRepresentation</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X87F71650795FE650">3.1-2 IsReducibleRepresentation</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7FF69B0D7DB36D73">3.2 <span class="Heading">Block Representations</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X847B7C45812A563B">3.2-1 EquivalentBlockRepresentation</a></span>
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<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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