On Sat, Aug 02, 2014 at 10:22:20AM +0200, Kurt Ewald wrote: > s4 := Group((1,2,3,4),(1,2));; s3 := Group((1,2,3),(1,2));; > > > > hom := GroupHomomorphismByImages( s4 , s3, GeneratorsOfGroup(s4), > [(1,2),(2,3)]; > > > > What is [(1,2),(2,3)] and how can I get this list in other examples? this is a list of generators of s3 so that the original generators of s4 are mapped to by hom.
If you know the kernel of the homomorphism then you can create the quotient group: e.g. in this case set gap> h:=Subgroup(s4,[(1,2)(3,4),(1,3)(2,4)]);; gap> s3f:=s4/h;; # this creates a finitely presented group # or better you can do gap> hom1:=ActionHomomorphism(s4,RightCosets(s4,h),OnRight);; gap> Image(hom1); # this is S_3 in a regular representation HTH, Dmitrii > > > > Best Regards > > > > Kurt Ewald > > > > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
