> < ^ Date: Sun, 02 Apr 2000 20:51:13 +0300
> < ^ From: Alexander B. Konovalov <alexk@mcs.st-and.ac.uk >
> < ^ Subject: Re: Maximal subgroups of SymmetricGroup(9)

Dear Gap-forum,
thank you very much for all who replied to my previous message concerning
Maximal subgroups of SymmetricGroup(9). I suppose it is worthwhile to note
what was the reason to calculate them. There is a problem 12.80 by
V.I.Suschansky in Kourovka notebook (I translate from Russian edition):
Describe all pairs (n,r) of natural n and r, such that the symmetric group
S_{n} contains maximal subgroup, isomorphic to S_{r}.
I have state a task for a graduate diploma project of my student to find
using GAP as much as possible of such pairs (n,r).
It is easy to obtain that for n<9 this pairs are only (3,2), (4,3), (5,4),
(6,5), (7,6) and (8,7). For n=9 we encountered the problem reported in my
previous message.
As far as I understand, it is obvious that the pair (n,n-1) obviously exist
for every n>2, and the problem is to prove that this is the only possible
case. Whether somebody already deal with this problem ?

Sincerely yours,
Alexander B. Konovalov,
Zaporozhye State University, Zaporozhye, Ukraine.
E-mail: konovalov@member.ams.org, algebra@hotmail.zp.ua

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