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 ⟶ FM ⟶ 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 ⟶ M does not factor as FM ⟶ P ⟶ 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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