[GAP Forum] Homomorphism

[Dima Pasechnik]

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));;
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> hom := GroupHomomorphismByImages( s4 , s3, GeneratorsOfGroup(s4),
> [(1,2),(2,3)];
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> 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


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> Best Regards
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> Kurt Ewald
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