> < ^ From:

^ Subject:

Dear all,

The following message is forwarded from Avital Oliver:

A few colleagues and I are working on an open conjecture in group theory

from the 70s, which is: All finite groups in which distinct conjugacy

classes have distinct sizes are either trivial or isomorphism to S_3.

During the 90s, this was proven if the group is also assumed to be solvable.We have been able to bring some progress on the problem in the case that

the group is not neccisarily solvable. In order for us to solve,

basically, the last case left for the paper to be ready, we need to check

that the conjecture holds for all subgroups of Aut(PSL(3,4)) wr S_k for 4

<= k <= 10. The way we have solved similar problems for other groups was

by using ConjugacyClassesSubgroups, and then passing one by one.The problem for larger groups (k >= 4) is that the group Aut(PSL(3,4)) wr

S_k is very large, and thus the calculation of the subgroups is very long,

and more troublesome very memory consuming. Since we don't really need to

calculate all the subgroups and then pass through all of them, I would

like to know if there is a way to iterate through the subgroups (upto

conjugation) *without* calculating them all at once... something like

iterating through SmallGroup(60, k) for all k - By Unbinding each time,

the memory that will be wasted will be minimal. If this is possible, we

could finish our final problem (which would not prove the conjecture,

though) by running GAP for enough time.Thanks in advance,

Avital.---

Avital Oliver

Department of Mathematics

Bar-Ilan University, Ramat-Gan, ISRAEL

+==========================+ Dr. John J. McDermott University of St Andrews BMS Building, North Haugh St Andrews, Fife KY16 9ST, Scotland Tel: +44 1334 463478 Mob: +44 7941 507531 +==========================+

> < [top]