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<div class="ChapSects"><a href="chap16.html#X85B05BBA78ED7BE2">16. <span class="Heading"> Meataxe modules</span></a>
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<h3>16. <span class="Heading"> Meataxe modules</span></h3>
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<td class="tdleft"><code class="code">DesuspensionMtxModule(M)</code></p>
<p>Inputs a meataxe module M over the field of p elements and returns an FpG-module DM. The two modules are related mathematically by the existence of a short exact sequence DM --> FM --> M with FM a free module. Thus the homological properties of DM are equal to those of M with a dimension shift.</p>
<p>(If G:=Group(M.generators) is a p-group then FM is a projective cover of M in the sense that the homomorphism FM --> M does not factor as FM --> P --> M for any projective module P.)</td>
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<td class="tdleft"><code class="code">FpG_to_MtxModule(M)</code></p>
<p>Inputs an FpG-module M and returns an isomorphic meataxe module.</td>
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<td class="tdleft"><code class="code"> GeneratorsOfMtxModule(M)</code></p>
<p>Inputs a meataxe module M acting on, say, the vector space V. The function returns a minimal list of row vectors in V which generate V as a G-module (where G=Group(M.generators) ).</td>
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