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.)

Inputs an FpG-module M and returns an isomorphic meataxe module.

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) ).