I am using GAP's CompatiblePairs and ExtensionRepresentatives functions to find the orbits on the second cohomology group (set of extensions) H^2(G;A) under the action of Aut(G) X Aut(A) for the trivial G-action of A. This works perfectly fine for most groups G and A, giving results that agree with my own calculations. However, for one particular pair of groups, it gives the wrong answer:
gap> G := CyclicGroup(4);; gap> A := TrivialGModule(G,GF(2));; gap> A1 := AutomorphismGroup(G);; gap> A2 := GL(1,2);; gap> D := DirectProduct(A1,A2);; gap> P := CompatiblePairs(G,A,D);; gap> M := ExtensionRepresentatives(G,A,P);; gap> List(M,IdGroup); [ [ 8, 2 ], [ 8, 2 ] ] The answer I expect is [8,1] and [8,2]. Just printing out extensions works fine: gap> G := CyclicGroup(4);; gap> A := TrivialGModule(G,GF(2));; gap> L := Extensions(G,A);; gap> List(L,IdGroup); [ [ 8, 2 ], [ 8, 1 ] ] The ExtensionRepresentatives works well for most other pairs I tested it with; I have appended some calculations to show this. Anybody have an idea if this is the result of a bug in the GAP code, or am I making some mistake in using the code? Vipul PS: Some calculations to show that ExtensionRepresentatives works well in most cases: For cyclic group of order 2 on cyclic group of order 2: gap> G := CyclicGroup(2);; gap> A := TrivialGModule(G,GF(2));; gap> A1 := AutomorphismGroup(G);; gap> A2 := GL(1,2);; gap> D := DirectProduct(A1,A2);; gap> P := CompatiblePairs(G,A,D);; gap> M := ExtensionRepresentatives(G,A,P);; gap> List(M,IdGroup); [ [ 4, 2 ], [ 4, 1 ] ] For Klein four-group on cyclic group of order 2: gap> G := ElementaryAbelianGroup(4);; gap> A := TrivialGModule(G,GF(2));; gap> A1 := AutomorphismGroup(G);; gap> A2 := GL(1,2);; gap> D := DirectProduct(A1,A2);; gap> P := CompatiblePairs(G,A,D); gap> M := ExtensionRepresentatives(G,A,P);; gap> List(M,IdGroup); [ [ 8, 5 ], [ 8, 2 ], [ 8, 3 ], [ 8, 4 ] ] _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
