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<div class="ChapSects"><a href="chap22_mj.html#X85B05BBA78ED7BE2">22 <span class="Heading"> Meataxe modules</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap22_mj.html#X7CFDEEC07F15CF82">22.1 <span class="Heading">  </span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap22_mj.html#X7AF88FB07F26E4F1">22.1-1 DesuspensionMtxModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap22_mj.html#X78679D82835AEC25">22.1-2 FpG_to_MtxModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap22_mj.html#X8594DD3B7F69265E">22.1-3 GeneratorsOfMtxModule</a></span>
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<h3>22 <span class="Heading"> Meataxe modules</span></h3>

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<h4>22.1 <span class="Heading">  </span></h4>

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<h5>22.1-1 DesuspensionMtxModule</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; DesuspensionMtxModule</code>( <var class="Arg">M</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a meataxe module <span class="SimpleMath">\(M\)</span> over the field of <span class="SimpleMath">\(p\)</span> elements and returns an FpG-module DM. The two modules are related mathematically by the existence of a short exact sequence <span class="SimpleMath">\(DM \longrightarrow FM \longrightarrow M\)</span> with <span class="SimpleMath">\(FM\)</span> a free module. Thus the homological properties of <span class="SimpleMath">\(DM\)</span> are equal to those of <span class="SimpleMath">\(M\)</span> with a dimension shift.</p>

<p>(If <span class="SimpleMath">\(G:=Group(M.generators)\)</span> is a <span class="SimpleMath">\(p\)</span>-group then <span class="SimpleMath">\(FM\)</span> is a projective cover of <span class="SimpleMath">\(M\)</span> in the sense that the homomorphism <span class="SimpleMath">\(FM \longrightarrow M\)</span> does not factor as <span class="SimpleMath">\(FM \longrightarrow P \longrightarrow M\)</span> for any projective module <span class="SimpleMath">\(P\)</span>.)</p>

<p><strong class="button">Examples:</strong> <span class="URL"><a href="../tutorial/chap11.html">1</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutIntro.html">2</a></span> , <span class="URL"><a href="../www/SideLinks/About/aboutTorAndExt.html">3</a></span> </p>

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<h5>22.1-2 FpG_to_MtxModule</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; FpG_to_MtxModule</code>( <var class="Arg">M</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs an FpG-module <span class="SimpleMath">\(M\)</span> and returns an isomorphic meataxe module.</p>

<p><strong class="button">Examples:</strong></p>

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<h5>22.1-3 GeneratorsOfMtxModule</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">&#an style='color: green'>8227; GeneratorsOfMtxModule</code>( <var class="Arg">M</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Inputs a meataxe module <span class="SimpleMath">\(M\)</span> acting on, say, the vector space <span class="SimpleMath">\(V\)</span>. The function returns a minimal list of row vectors in <span class="SimpleMath">\(V\)</span> which generate <span class="SimpleMath">\(V\)</span> as a <span class="SimpleMath">\(G\)</span>-module (where G=Group(M.generators) ).</p>

<p><strong class="button">Examples:</strong></p>


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