Dear GAP Forum

Cinzia Casagrande wrote:

> I have the following problem: I have a semigroup H inside a free group G.
> G is of finite rank but clearly infinite. H is given by some generators,
> but they could be redundant or have some relations. I would like to know
> the relations between these generators in the semigroup H, or at least to
> know which generators are necessary to get H. Is this possible in some
> way?
I would like to add that what you need is a SAGBI-basis (subalgebra analog of
Groebner basis for subalgebras) of more exactly, Factor- SAGBI basis, because
Free group is not free as a semigroup. The algorithm exists, but I do not know
available implementations in noncommutative case (though we also plan to have
it) - there are too many complications in the non-commutative case.

With best regards
Victor Ufnarovski