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<title>GAP (LAGUNA) - Chapter 5: The Modular Isomorphism Problem</title>
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<h3>5. <span class="Heading">The Modular Isomorphism Problem</span></h3>
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<h4>5.1 <span class="Heading">Known results on MIP</span></h4>
<p>???????????????????????????????????</p>
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<h4>5.2 <span class="Heading">Invariants determined by group algebras</span></h4>
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<h5>5.2-1 SandlingFactorGroup</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> SandlingFactorGroup</code>( <var class="Arg">G</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><b>Returns: </b>factorgroup</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s2ss2" name="s2ss2"></a></p>
<h5>5.2-2 JenningsFactors</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> JenningsFactors</code>( <var class="Arg">G</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><b>Returns: </b>list of lists of IdGroup</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s2ss3" name="s2ss3"></a></p>
<h5>5.2-3 NumberOfConjugacyClassesPPowers</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> NumberOfConjugacyClassesPPowers</code>( <var class="Arg">G</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><b>Returns: </b>list of integers</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s2ss4" name="s2ss4"></a></p>
<h5>5.2-4 ClassSumNumbers</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> ClassSumNumbers</code>( <var class="Arg">G</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><b>Returns: </b>list of integers</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s2ss5" name="s2ss5"></a></p>
<h5>5.2-5 QuillenSeries</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> QuillenSeries</code>( <var class="Arg">G</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><b>Returns: </b>list of integers</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s2ss6" name="s2ss6"></a></p>
<h5>5.2-6 RoggenkampParameter</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> RoggenkampParameter</code>( <var class="Arg">G</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><b>Returns: </b>integer</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s2ss7" name="s2ss7"></a></p>
<h5>5.2-7 RoggenkampParameterForNormalSubset</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> RoggenkampParameterForNormalSubset</code>( <var class="Arg">G, S</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>integer</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s2ss8" name="s2ss8"></a></p>
<h5>5.2-8 KernelSize</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> KernelSize</code>( <var class="Arg">FG[, n, m, k]</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p><b>Returns: </b>integer or fail</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss0" name="s3ss0"></a></p>
<h4>5.3 <span class="Heading">MIP testing tools</span></h4>
<p><a id="s3ss1" name="s3ss1"></a></p>
<h5>5.3-1 PrintMIPInvariants</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> PrintMIPInvariants</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss2" name="s3ss2"></a></p>
<h5>5.3-2 PrintMIPInvariantsTable</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> PrintMIPInvariantsTable</code>( <var class="Arg">list, filename</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>text file generated in the current directory</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss3" name="s3ss3"></a></p>
<h5>5.3-3 MIPInvariantsRecord</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> MIPInvariantsRecord</code>( <var class="Arg">G</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>record</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss4" name="s3ss4"></a></p>
<h5>5.3-4 MIPInvariantsLibrary</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> MIPInvariantsLibrary</code>( <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>text file generated in the current directory</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss5" name="s3ss5"></a></p>
<h5>5.3-5 MIPInvariantsLibraryClassification</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> MIPInvariantsLibraryClassification</code>( <var class="Arg">invlib, mode</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>list of lists and (optionally) a text file generated in the current directory</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss6" name="s3ss6"></a></p>
<h5>5.3-6 KernelSizeTest</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> KernelSizeTest</code>( <var class="Arg">FG, FH</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>a list of parameters and kernel sizes or fail</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss7" name="s3ss7"></a></p>
<h5>5.3-7 JenningsLieAlgebraTest</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> JenningsLieAlgebraTest</code>( <var class="Arg">FG, FH</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>true or false</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss8" name="s3ss8"></a></p>
<h5>5.3-8 MIPSplittingByKernelSize</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> MIPSplittingByKernelSize</code>( <var class="Arg">list, no, mode</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>text file generated in the current directory</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss9" name="s3ss9"></a></p>
<h5>5.3-9 MIPSplittingByJenningsLieAlgebra</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> MIPSplittingByJenningsLieAlgebra</code>( <var class="Arg">list, no, mode</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p><b>Returns: </b>text file generated in the current directory</p>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
<p><a id="s3ss10" name="s3ss10"></a></p>
<h5>5.3-10 MIPSplittingReport</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">> MIPSplittingReport</code>( <var class="Arg">list</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>???????????????????????????????????</p>
<table class="example">
<tr><td><pre>
</pre></td></tr></table>
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