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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.)

Me too!

> 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?)

See above.

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.

Joachim Neubueser

neubueser@math.rwth-aachen.de

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