[GAP Forum] Join of two subgroups (as FP groups)

[dmitrii.pasechnik at cs.ox.ac.uk]

On Thu, Nov 08, 2018 at 04:13:54PM +0000, Alexander Konovalov wrote:
> The quotient of the free group on the union of their generators by the union of their relations will correspond to a free product of H1 and H2 - is this the group you intend to construct?
> 

It seems William is talking about the amalgamated by $H_1 \cap H_2$ free
product of $H_1$ and $H_2$.

Best,
Dima
> 
> 
> > On 7 Nov 2018, at 17:11, William Giuliano <williamgiuliano00 at gmail.com> wrote:
> > 
> > Dear Forum,
> >                     suppose I have two subgroups H1 and H2 of a (matrix)
> > group G, such that their join is the whole of G. When I convert H1 and H2
> > into Fp groups, and consider the quotient of the free group on the union of
> > their generators by the union of their relations, how should the resulting
> > Fp group be considered in GAP?
> > 
> > Thank you very much
> > William