[GAP Forum] homomorphism construction wanted

[Max Horn]

Dear Graham,

> On 12. Apr 2020, at 14:37, Ellis, Grahamj <graham.ellis at nuigalway.ie> wrote:
> 
> Dear GAP Community,
> 
> Is there a way to construct a group homomorphism using a variant of the function
> 
> f:=GroupHomomorphismByFunction(G,H,x->function(x))

Minor side remark:  instead of writing 
  x->function(x)
you can just write
  function

> 
> for which
> 
> ImageElm(f,x)
> 
> does not test to see if x lies in G?

But ImageElm in the above setting never tests if x lies in G. It directly calls the function you provided:

gap> f:=GroupHomomorphismByFunction(G,H,x->x^2);;
gap> Display(ApplicableMethod(ImageElm, [f, G.1]));
function ( map, elm )
    return map!.fun( elm );
end

Any membership tests you are seeing must be caused by something else.

Cheers
Max

>  Here function(x) is a well-defined function for x in G, but G is a group for which I don't have a membership test.
> 
> Thanks,
> 
> Graham
> 
> 
> School of Mathematics, Statistics & Applied Mathematics
> National University of Ireland, Galway
> tel: 091 493011
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