[GAP Forum] Question on action homomorphism

[Alexander Hulpke]

Dear Gap-Forum,

On Jun 26, 2014, at 6/26/14 11:10, Pierre-Alain BOURDIL <pabourdi at laas.fr> wrote:

> 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);

Neither of these are action homomorphisms, as the domain is not closed under the group (e.g. [2,3] is not in).

We will improve the sanity tests for future versions so that an error message will be given instead of a wrong result.

Regards,

  Alexander Hulpke

> 
> 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>
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