Re: Groups of order 99
From: Jim Heckman (wnzrfeurpxzna_at_lnubb.pbz.invalid)
Date: 07/07/04
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Date: Wed, 7 Jul 2004 06:21:21 GMT
On 6-Jul-2004, "Julien Santini" <santini.julien@wanadoo.fr>
wrote in message <cces6s$j7h$1@news-reader4.wanadoo.fr>:
> Thanks for quoting Jim's argument (surprisingly it hadn't appeared in my
> newsreader), which is not only much simpler but -I think- more general
> too,
> in a way. (It must be much more tedious to compute all the possible
> cardinals of Aut(G) when dealing with p-Groups, and I'm not sure this
> method
> always work anyways; however, when one of the two given subgroups is not
> normal, it sounds like the result doesnt hold anymore. I'm going to check
> this assertion).
If by "the result" you mean that the Sylow p-subgroups must
commute, it certainly does *not* hold anymore if they're not
normal. Smallest counter-example: S_3.
-- Jim Heckman
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