Ralf Dentzer asks:
> The GAP function FrattiniSubgroup is not included in the manual.
> I think this is due to the fact that it only works for p-groups.
> Can I hope for this function to work for general AG groups
> or even all finite groups sometime?
This function FrattiniSubgroup(G) does in fact exist, and it works
only for p-groups which moreover must be given as AG-groups - it will
not work for a p-group that is given by generating permutations for
instance. The reason that it is not included in the manual (and
possibly extended by a brute force method in all other cases) is the
following: Charles Leedham-Green has proposed the use of a very
special kind of AG-presentations for arbitrary soluble groups which
among other things will facilitate the computation of all maximal
subgroups of a soluble group and hence of course also the Frattini
subgroup. A student here in Aachen, Bettina Eick, is at present
implementing this and related proposals and we hope that with the next
release of GAP her programs which indeed will give some further new
functions and some improvements of performnce for some existing ones
will be included. At that time then we shall try to have a general
function FrattiniGroup which in the cases where we do not know better
will resort to brute force.
Ralf Dentzer continues:
> (I had some hopes that this would be included in version 3.2.)
> At the moment I can compute the frattini subgroup by brute force
> using ConjugacyClassesSubgroups, but is there a better way?
> (And should this brute force method be included in GAP?)
Thanks for the question, we are happy to inform about what is going on
and encourage others to do the same with work going on with them.