> < ^ Date: Tue, 14 May 2002 11:18:34 +0100
> < ^ From: John J McDermott <jjm@dcs.st-and.ac.uk >
^ Subject: Fwd: How to iterate through subgroups of a group

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.

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
+==========================+
```

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