  
  [1X22 [33X[0;0YMeataxe modules[133X[101X
  
  
  [1X22.1 [33X[0;0Y [133X[101X
  
  [1X22.1-1 DesuspensionMtxModule[101X
  
  [33X[1;0Y[29X[2XDesuspensionMtxModule[102X( [3XM[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  meataxe  module  [22XM[122X  over  the  field of [22Xp[122X elements and returns an
  FpG-module  DM.  The two modules are related mathematically by the existence
  of  a  short  exact  sequence  [22XDM  ⟶  FM ⟶ M[122X with [22XFM[122X a free module. Thus the
  homological properties of [22XDM[122X are equal to those of [22XM[122X with a dimension shift.[133X
  
  [33X[0;0Y(If  [22XG:=Group(M.generators)[122X  is a [22Xp[122X-group then [22XFM[122X is a projective cover of [22XM[122X
  in  the sense that the homomorphism [22XFM ⟶ M[122X does not factor as [22XFM ⟶ P ⟶ M[122X for
  any projective module [22XP[122X.)[133X
  
  [33X[0;0Y[12XExamples:[112X             1             ([7X../tutorial/chap11.html[107X) ,            2
  ([7X../www/SideLinks/About/aboutIntro.html[107X) ,                                 3
  ([7X../www/SideLinks/About/aboutTorAndExt.html[107X) [133X
  
  [1X22.1-2 FpG_to_MtxModule[101X
  
  [33X[1;0Y[29X[2XFpG_to_MtxModule[102X( [3XM[103X ) [32X function[133X
  
  [33X[0;0YInputs an FpG-module [22XM[122X and returns an isomorphic meataxe module.[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
  [1X22.1-3 GeneratorsOfMtxModule[101X
  
  [33X[1;0Y[29X[2XGeneratorsOfMtxModule[102X( [3XM[103X ) [32X function[133X
  
  [33X[0;0YInputs  a  meataxe module [22XM[122X acting on, say, the vector space [22XV[122X. The function
  returns  a  minimal  list of row vectors in [22XV[122X which generate [22XV[122X as a [22XG[122X-module
  (where G=Group(M.generators) ).[133X
  
  [33X[0;0Y[12XExamples:[112X[133X
  
