Alexander Hulpke <hulpke@...> writes:
>
>
> Dear Forum,
>
> On Oct 10, 2013, at 10/10/13 11:19, Sopsku <rrburns@...> wrote:
>
> > Dear forum,
> >
> > I am having some difficulty understanding projections and semidirect
products.
> > Now I would like to do soemthing similar for a semidirect product group, e.g
> >
> > a:=AutomorphismGroup(g);
> > s:=SemidirectProduct(a,g);
> >
> > but now
> > Projection(s,1);
> > fails.
> >
> > Can I use the GAP Projections to do a decomposition similar to the direct
> > product example above?
>
> According to the manual, for a semidirect product N:S
> Projection(s)
> returns the projection onto S, there is no projection onto N which is a
group homomorphism (and thus no
> numeric parameter to Projection).
>
> If you want to get an N-part of a product element g, you could divide off
the canonical representative for the
> projection image, for example:
>
> PreImagesRepresentative(Embedding(s,1),
g/Image(Embedding(s,2),Image(Projection(s),g));
>
> Regards,
>
> Alexander Hulpke
>
Sorry for being so dense, but I do not fully understand the command and it
fails so I am not quite sure what Prof. Hulple intended. I did try the
following:
npart1:=function(elm)
return Image(e1,Image(p,elm))^p;
end;
npart2:=function(elm)
return PreImagesRepresentative(e2,elm/Image(e1,Image(p,elm)));
end;
PrintArray(List(Elements(S),e->[npart1(e),npart2(e)]));
Which is more or less what I think I am looking for. Is this kind of what
Prof. Hulpke intended.
Again thank you for any help or comments.
Ron
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