Re: simple proof for a group theory question?

From: Marian (marian_at_fasttelco.com)
Date: 09/28/04 

Date: Tue, 28 Sep 2004 13:30:08 +0000 (UTC)

Thanks a lot, Serge and Derek, both proofs are fine. "Elementary" was
meant to mean elementary for a first year student, not yet exposed to
group actions.

I've got this little thing as a particular case of a more general
setting: if A is any automorphism group of a finite group G, then
every subgroup of C_G(A) acts by translation on the set of orbits of A
in G. The group in question, that Serge indicated, is just the
stabilizer of the orbit of x in that action
(if one takes A to be the inner autos and Z as C_G(A)). This is what
lies behind that little divizibility result.

All the best, Marian