‣ DesuspensionMtxModule( M ) | ( function ) |
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 \(DM \longrightarrow FM \longrightarrow M\) with \(FM\) a free module. Thus the homological properties of \(DM\) are equal to those of \(M\) with a dimension shift.
(If \(G:=Group(M.generators)\) is a \(p\)-group then \(FM\) is a projective cover of \(M\) in the sense that the homomorphism \(FM \longrightarrow M\) does not factor as \(FM \longrightarrow P \longrightarrow M\) for any projective module \(P\).)
‣ FpG_to_MtxModule( M ) | ( function ) |
Inputs an FpG-module \(M\) and returns an isomorphic meataxe module.
Examples:
‣ GeneratorsOfMtxModule( M ) | ( function ) |
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) ).
Examples:
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