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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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