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

[William Giuliano]

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

[Alexander Konovalov]

Dear William,

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?

Best wishes
Alexander

Post by William Giuliano
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
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[d***@cs.ox.ac.uk]

Post by Alexander Konovalov
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

Post by Alexander Konovalov

Post by William Giuliano
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