Sophie

Sophie

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gap-system-4.4.12-5mdv2010.0.x86_64.rpm

  
  16. Meataxe modules
  
      | DesuspensionMtxModule(M) 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.) | 
      | FpG_to_MtxModule(M) Inputs an FpG-module M and returns an isomorphic meataxe module.                                                                                                                                                                                                                                                                                                                                                                                                                                    | 
      |  GeneratorsOfMtxModule(M) 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) ).                                                                                                                                                                                                                                                                                                          |