Dear forum,

Robert Scarth asked

When I ask GAP for a presentation of a subgroup H, of G, say it
returns a presentation on generators _x<i>. For any i, can GAP give
me an expression for _x<i> in terms of the generators of G?

In fact, GAP 3.4.3 cannot do this.

However, the new release GAP 3.4.4 (which has been announced
to be available just one week ago) has been extended such
that now, whenever you call the function PresentationSubgroup,
the resulting presentation record P will involve an additional
component P.primaryGeneratorWords which provides words in the
generators of G for all primary generators occurring in the
subgroup presentation.

The new facilities are described in the chapter on Finitely
Presented Groups in version 3.4.4 of the GAP manual.

My suggestion is that you should try to get hands on the new
version as soon as possible. I assume that will solve your
problem.

Best regards,

Volkmar Felsch, Aachen