[GAP Forum] Is there a way to teach GAP that a particular map is injective or surjective?

[Will Chen]

Dear Forum,

Suppose I have two groups G, H, and a homomorphism f : G --> H, defined
using "GroupHomomorphismByImages".

Suppose I know that f is surjective, and that moreover there is a
generating set X of H for which I can provide explicit preimages in G.

Is there a way of giving GAP this information?

Ie, in my situation, trying to call the PreImage operation on f sometimes
takes over 5 minutes (at which point I opted to break), but presumably if I
can give GAP explicit preimages for generators, it can then decompose every
element of H as a word in those generators, and use the explicit preimages
to find a preimage for that word.

If necessary, I'm happy to assume that G,H are finitely presented.

- Will

-- 

William Chen
NSF Postdoctoral Fellow, Department of Mathematics
McGill University,
Montreal, Quebec, H3A 0B9
oxeimon at gmail.com