GAP (HAP commands) - Chapter 22: Meataxe modules

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22 Meataxe modules
22.1
22.1-1 DesuspensionMtxModule
22.1-2 FpG_to_MtxModule
22.1-3 GeneratorsOfMtxModule

### 22 Meataxe modules

#### 22.1

##### 22.1-1 DesuspensionMtxModule

`‣ 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 \(P\).)

Examples: 1 , 2

##### 22.1-2 FpG_to_MtxModule

`‣ FpG_to_MtxModule`( M ) | ( function )

Inputs an FpG-module \(M\) and returns an isomorphic meataxe module.

Examples:

##### 22.1-3 GeneratorsOfMtxModule

`‣ 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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