Dear Leonard,

Thank you very much for the error report. We will correct this in a future
fix.

What is a good way in GAP3 of computing with finitely generated (but
not necessarily finite) abelian groups? The things I need to do now is
determine structure efficiently when I have very many relations (even
forming FreeGroup(n)/rels can pack up) and to work efficiently with a
quotient (by a given subgroup).

At the moment neither GAP3, nor GAP4 contain much functionality for infinite
groups. GAP4 will get it in the future, but momentarily the finitely
presented groups code in GAP4 is still being worked on.

I don't know what you want to do exactly, but I suppose the easiest
solution would be to represent the groups as quotients of the free abelian
group by relator matrices and compute for example the Smith normal form to
determine the structure.
(If you need further help to implement this please write.)

Best wishes,

Alexander