Quelle  6.16A.txt

gap> G1:=AlternatingGroup(5);;
gap> G2:=SymmetricGroup(5);;
gap> f:=GroupHomomorphismByFunction(G1,G2,x->x);;
gap> pi:=PermToMatrixGroup(G2,5);;
gap> R1:=ResolutionFiniteGroup(G1,7);;
gap> R2:=ResolutionFiniteGroup(G2,7);;
gap> F:=EquivariantChainMap(R1,R2,f);;
gap> C:=HomToIntegralModule(F,pi);;
gap> c:=Cohomology(C,6);
[ g1, g2, g3 ] -> [ id, id, g3 ]

gap> AbelianInvariants(Kernel(c));
[ 2, 2 ]
gap> AbelianInvariants(Range(c)/Image(c));
[ 2, 3 ]