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<h1>CRIME</h1>


<h2>A <strong class="pkg">GAP</strong> Package to Calculate Group Cohomology and Massey Products</h2>

<p>
    1.6</p>

<p>
    17 March 2022
  </p>

</div>
<p><b>
    Marcus Bishop



  </b>
<br />Email: <span class="URL"><a href="mailto:marcus.bishop@gmail.com">marcus.bishop@gmail.com</a></span>
<br />Homepage: <span class="URL"><a href="http://math.uic.edu/~marcus">http://math.uic.edu/~marcus</a></span>
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<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2006, 2007 Marcus Bishop</p>

<p><strong class="pkg">CRIME</strong> is free software which is distributed under the GNU Public Licence, version 2, and may be redistributed under the GNU Public Licence, version 2 or later (at your preference). See the file COPYING for detailed information</p>

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<h3>Acknowledgements</h3>
<p>This project would not have been possible without Jon Carlson. Jon devised the algorithms used by <code class="keyw">ProjectiveResolution</code>, <code class="keyw">CohomologyGenerators</code>, and <code class="keyw">CohomologyRelators</code>, having already implemented them in <strong class="pkg">Magma</strong>, and shared these programs with me.</p>

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

<div class="ContChap"><a href="chap1.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X86C437C47F3988E8">1.1 <span class="Heading">Installation and Loading</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1.html#X83499FE181F08DC9">1.2 <span class="Heading">For Further Information</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2.html#X86A9B6F87E619FFF">2 <span class="Heading">Usage</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X85BF21B17BF76907">2.1 <span class="Heading">Cohomology Objects</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8716E7657F9683B7">2.1-1 CohomologyObject</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7FEB30657DDEFE44">2.2 <span class="Heading">Minimal Projective Resolutions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8273999C7B352F22">2.2-1 ProjectiveResolution</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7AF313D387F6BA22">2.2-2 BoundaryMap</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X78C37B2E7D297FC5">2.3 <span class="Heading">Cohomology Generators and Relators</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X81F141187B0EC653">2.3-1 CohomologyGenerators</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X812BE8E983DC20BC">2.3-2 CohomologyRelators</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X87C9251687CD4247">2.4 <span class="Heading">Tests for Completion</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X80B6849C835B7F19">2.5 <span class="Heading">Cohomology Rings</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7B77337486380998">2.5-1 CohomologyRing</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7D8EA4528082A74D">2.5-2 IsHomogeneous</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X826A861E7E7D944E">2.5-3 Degree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X813A8E4C7D4C9FBD">2.5-4 LocateGeneratorsInCohomologyRing</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7E21853583D6D86D">2.6 <span class="Heading">What Happens if <code class="keyw">n</code> Isn't
Big Enough?</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X837261007B39795C">2.7 <span class="Heading">Induced Maps</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X8608BD148307390B">2.7-1 InducedHomomorphismOnCohomology</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X80798C0979D4E9DC">2.7-2 SubgroupInclusion</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7B541EB97BAB36D7">2.8 <span class="Heading">Massey Products</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2.html#X7E3023CE86641F9E">2.8-1 MasseyProduct</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapA.html#X82113B3184F76F58">A <span class="Heading">Some Benchmarks</span></a>
</div>
<div class="ContChap"><a href="chapB.html#X7BC2C62E7A8CC2B9">B <span class="Heading">Leisure and Recreation: Cohomology Rings
of all Groups of Size 16</span></a>
</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>
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