[GAP Forum] FactorGroup of permutation groups

[tkohl at math.bu.edu]

Dear Forum, Alexander,

> Dear Forum, Dear Tim Kohl,
> 
> If N, H are permutation groups with H normal in N
> and one computes FactorGroup(N,H) the result is expressed
> in terms of generators and relations.
> 
> I suspect it is a PcGroup (which happens i factor is solvable). Otherwise it will be a permutation group.
> 
> Is there a way to
> correlate the generators of FactorGroup(N,H) with a
> transversal of H in N?
> 
> So you probably want the permutation action of N on the cosets of H. You can get it as `FactorCosetAction(N,H)` with the numbering of points corresponding to `RightTransversal(N,H)`.

I guess my natural question (betraying a bit of ignorance) is how can I utilize this Action?

And if I have a subgroup of FactorGroup(N,H) can I look at the resulting action on the level of cosets?

Thank you.

	-T

> 
> All the best,
> 
>   Alexander Hulpke
> 
> The reason I'm asking is that N acts transitively
> on a collection of groups with H as the stabilizer
> and I want to study the induced action of N/H (and most
> importantly subgroups thereof) as it is substantially smaller.
> 
> Thanks.
> 
> -Tim K.
> 
> - Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hulpke at colostate.edu, http://www.math.colostate.edu/~hulpke
>