Dear Gap-Forum: I have the following sort of computation which I would like
to do using GAP: I am given a finitely presented group P, a surjective
homomorphism f from P to a finite group G (given, as, say a subgroup of
a permutation group), and a subgroup H of G. I would like to compute the
abelianization of the inverse image of H under f. I realize that this
could be done using the command `AbelianInvariantsSubgroupFpGroup', once
generators have been chosen for the subgroup f^-1(H). Finding
generators is easy `by hand' starting from a transversal of f^-1(H) in P;
the question is how to find such transversal using GAP. The key point
seems to be pulling back a transversal of H in G to P. Does anyone have
any pointers on how this can be done in GAP?
My second question is related: has the Fox free calculus been
implemented in GAP (or something whose output is accessible to GAP)? From
a computational standpoint, would it be better to use the command
AbelianInvariants... (assuming that the question in the previous
paragraph has a reasonable answer)?
Thanks for any input.