Dear Gap Forum members,
On July 15 Toni Gaglione und David Joyner wrote:
> Given a finitely generated free group
> F and a fixed sequence c1, c2, ... of basic commutators (as in M Hall,
> chapter 11), can GAP reduce an arbitrary non-trivial element in F to its
> normal form in terms of these basic commutators modulo F_n, where
> F_n is the nth term of the lower central series of F?
There is no routine for doing that in the current GAP release. However, I had
written a couple of simple GAP routines for computing basic commutators up to
a given weight a while ago. When I saw the above request I added a routine
for computing the normal form above for the special case when the word in F is
a product of the generators (i.e. no inverses are involved). I am happy to
supply the code to everone who is interested. There are hardly any comments
in the code and it is a fairly straightforward implementation of Chapter 11 of
M.Hall's book. It would need some polishing before I would feel comfortable
to make it generally available.
If there is sufficient interest I would be interested in extending the package
and give more thought to perfomance issues. Adding the handling of inverses
is clear from the theoretical point of view, but it needs quite a bit more
code which is the main reason why I didn't implement it at this stage.
All the best, Werner Nickel.