Dear Mrs. and Mr. Forum,
recently Evelyn Hart asked you whether GAP can handle group rings.
She toldI'm interested in the group ring Z[\pi] where Z is the integers and \pi is the group on four generators, a,b,c,d with one relation a b 1/a 1/b c d 1/c 1/d.
At the moment GAP has no facilities to do computations with
group rings. In the near future we will introduce group ring
data structures. But there is no aim to deal with group rings
of finitely presented groups, since for arithmetic calculations
with group ring elements it is necessary to decide at least
whether or not two group elements are equal, for which there is
no general algorithmic method with finitely presented groups.
Sorry that GAP does not provide the expected tools in any
straightforward way. However, does anybody have ideas how
to attack problems of this kind algorithmically?
How about working with the group ring over a finitely generated free
(non) abelian group?