In his message, John Neil asked:
>
> I have need to do calculations with group rings of ag-groups. Does GAP know
> how to deal with this already or am I looking at defining a new domain? If
> someone has already done something with this, I would appreciate knowing what
> it is.
>
Group Rings are not a built-in object. If the groups, in which you want to
compute are not too big (basically this means, that you can keep a list of
all group elements in memory at the same time and you are prepared to wait
for multiplications --- multiplication is done by simple distributive
expansion of sums, thus requires a lot of products to be computed), I can
provide some basic routines, I wrote some time ago. They provide a group
algebra as an vector space of dimension $|G|$, the basis corresponding to
the group elements. Thus elements are represented as sums of group elements.
Supported operations are almost only the basic ring operations +, -, *.

Alexander Hulpke