<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> 
</Description>

























































































































</ManSection>

<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>

