Dear Forum,
On Oct 10, 2013, at 10/10/13 11:19, Sopsku <rrbu...@cox.net> 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
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