[GAP Forum] Question on action homomorphism

[Pierre-Alain BOURDIL]

Hi,
Suppose the following groups and ActionHomomorphisms :
gap> G:=Group((1,2));

gap> H := Group((3,4));

gap> hom := ActionHomomorphism(G,[[1,3],[2,4]],OnSets);

gap>  hom2 := ActionHomomorphism(H,[[1,3],[2,4]],OnSets);

Asking for Image(hom), i get :
gap> Image(hom);
Group([ (1,2) ])

But when i try Image(hom2), i get :
gap> Image(hom2);
Group([ () ])


I can't figure out why the image of hom2 is an empty group,  i expect a 
S_2 group for both homomorphism. Is anyone here can explain this  ?

+

-- 
Pierre-Alain BOURDIL
pabourdi at laas.fr <mailto:pabourdi at laas.fr>
pierre-alain.bourdil at fr.thalesgroup.com 
<mailto:pierre-alain.bourdil at fr.thalesgroup.com>