hi, i think i found a bug with the group homomorphisms. AB is not a group in spite of f: AB --> B is a group homomorphism.
Alper gap> A:=Group((1,2,3,4)); Group([ (1,2,3,4) ]) gap> elA:=Elements(A); [ (), (1,2,3,4), (1,3)(2,4), (1,4,3,2) ] gap> B:=Subgroup(A,[elA[3]]); Group([ (1,3)(2,4) ]) gap> A=B; false gap> IsSubgroup(A,B); true gap> AB:=Cartesian(A,B); [ [ (), () ], [ (), (1,3)(2,4) ], [ (1,2,3,4), () ], [ (1,2,3,4), (1,3)(2,4) ], [ (1,3)(2,4), () ], [ (1,3)(2,4), (1,3)(2,4) ], [ (1,4,3,2), () ], [ (1,4,3,2), (1,3)(2,4) ] ] gap> f:=GroupHomomorphismByFunction(AB,B,x->x^2); MappingByFunction( [ [ (), () ], [ (), (1,3)(2,4) ], [ (1,2,3,4), () ], [ (1,2,3,4), (1,3)(2,4) ], [ (1,3)(2,4), () ], [ (1,3)(2,4), (1,3)(2,4) ], [ (1,4,3,2), () ], [ (1,4,3,2), (1,3)(2,4) ] ], Group( [ (1,3)(2,4) ]), function( x ) ... end ) gap> IsGroupHomomorphism(f); true gap> IsGroup(AB); false gap> Image(f); Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 1st choice method found for `GeneratorsOfMagmaWithInverses' on 1 arg\ uments called from GeneratorsOfGroup( PreImagesRange( map ) ) called from MappingGeneratorsImages( hom ) called from ImagesSource( arg[1] ) called from <function>( <arguments> ) called from read-eval-loop Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
