Thank you, Jacob, for your help with homomorphisms in GAP. I have
still some questions:
You are right, I am not only interested in injective
homomorphisms, but rather all of them. My problem is that the
groups where I look for homomorphic images are not finite.
The groups are finitely generated and all relators have the
form: a b = b c for generators a,b,c. But there is certainly
still an algorithm for detecting all homomorphic images of such
a group G to a given symmetric group S: There are only finitely
many possibilities in mapping the generators of G to the
generators of S and one such possibility describes a map
entirely.
I could not get the example Jacob sent to work, because
the group g1 was not defined.

Stephan Rosebrock

rosebro@math.uni-frankfurt.de