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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.

Daniel Ruberman

ruberman@max.math.brandeis.edu ruberman@binah.cc.brandeis.edu

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