<Chapter><Heading> Meataxe modules</Heading>
<Table Align="|l|" >
<Row>
<Item>
<Index>DesuspensionMtxModule</Index>
<C>DesuspensionMtxModule(M)</C>
<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>.)
</Item>
</Row>
<Row>
<Item>
<Index>FpG&uscore;to&uscore;MtxModule</Index>
<C>FpG&uscore;to&uscore;MtxModule(M)</C>
<P/>
Inputs an FpG-module <M>M</M> and returns an isomorphic meataxe module.
</Item>
</Row>
<Row>
<Item>
<Index>GeneratorsOfMtxModule</Index>
<C>GeneratorsOfMtxModule(M)</C>
<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) ).
</Item>
</Row>
</Table>
</Chapter>
