<Chapter><Heading> Meataxe modules</Heading> <Section><Heading> &nbsp;</Heading> 
<ManSection> <Func Name="DesuspensionMtxModule" Arg="M"/> <Description> <P/> Inputs a meataxe module <M>M</M> over the field of <M>p</M> elements and returns an FpG-module DM. The two modules are related mathematically by the existence of a short exact sequence <M>DM \longrightarrow FM \longrightarrow M</M> with <M>FM</M> a free module. Thus the homological properties of <M>DM</M> are equal to those of <M>M</M> with a dimension shift. <P/> (If <M>G:=Group(M.generators)</M> is a <M>p</M>-group then <M>FM</M> is a projective cover of <M>M</M> in the sense that the homomorphism <M>FM \longrightarrow M</M> does not factor as <M>FM \longrightarrow P \longrightarrow M</M> for any projective module <M>P</M>.) <P/><B>Examples:</B> <URL><Link>../tutorial/chap11.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutIntro.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTorAndExt.html</Link><LinkText>3</LinkText></URL>&nbsp;
</Description> </ManSection> 
<ManSection> <Func Name="FpG_to_MtxModule" Arg="M"/> <Description> <P/> Inputs an FpG-module <M>M</M> and returns an isomorphic meataxe module. <P/><B>Examples:</B> 
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<ManSection> <Func Name="GeneratorsOfMtxModule" Arg="M"/> <Description> <P/> Inputs a meataxe module <M>M</M> acting on, say, the vector space <M>V</M>. The function returns a minimal list of row vectors in <M>V</M> which generate <M>V</M> as a <M>G</M>-module (where G=Group(M.generators) ). <P/><B>Examples:</B> 
</Description> </ManSection> </Section> </Chapter>