<?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 (LAGUNA) - Chapter 5: The Modular Isomorphism Problem</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" /> </head> <body> <div class="pcenter"><table class="chlink"><tr><td class="chlink1">Goto Chapter: </td><td><a href="chap0.html">Top</a></td><td><a href="chap1.html">1</a></td><td><a href="chap2.html">2</a></td><td><a href="chap3.html">3</a></td><td><a href="chap4.html">4</a></td><td><a href="chap5.html">5</a></td><td><a href="chapBib.html">Bib</a></td><td><a href="chapInd.html">Ind</a></td></tr></table><br /></div> <p><a id="s0ss0" name="s0ss0"></a></p> <h3>5. <span class="Heading">The Modular Isomorphism Problem</span></h3> <p><a id="s1ss0" name="s1ss0"></a></p> <h4>5.1 <span class="Heading">Known results on MIP</span></h4> <p>???????????????????????????????????</p> <p><a id="s2ss0" name="s2ss0"></a></p> <h4>5.2 <span class="Heading">Invariants determined by group algebras</span></h4> <p><a id="s2ss1" name="s2ss1"></a></p> <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> <div class="pcenter"> <table class="chlinkprevnext"><tr><td><a href="chap0.html">Top of Book</a></td><td><a href="chap4.html">Previous Chapter</a></td><td><a href="chapBib.html">Next Chapter</a></td></tr></table> <br /> <div class="pcenter"><table class="chlink"><tr><td class="chlink1">Goto Chapter: </td><td><a href="chap0.html">Top</a></td><td><a href="chap1.html">1</a></td><td><a href="chap2.html">2</a></td><td><a href="chap3.html">3</a></td><td><a href="chap4.html">4</a></td><td><a href="chap5.html">5</a></td><td><a href="chapBib.html">Bib</a></td><td><a 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