[GAP Forum] bug with group homomorphism

[Alper Odabaş]

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>