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Re: algebra with order 2p.

Subject: Re: algebra with order 2p.
From: Arturo Magidin
Date: Thu, 14 Sep 2006 16:32:17 +0000 UTC
Newsgroups: sci.math
In article <eebvnd$ta$1@xxxxxxxxxxxxxxxx>,
mina_world <mina_world@xxxxxxxxxxx> wrote:

>yes, i see.
>maybe, i need the lemma.
>
>lemma) Let G be a group containing normal subgroups H and K
>such that H /\ K ={e} and H \/ K =G.
>then G is isomorphic to H x K.
>(H \/ K is the smallest subgroup of G containing HN.)

You mean, containing HK.

You hardly need that much. Just show that if H and K are normal, and
H/\K={e}, then HK is isomorphic to H x K. 


-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes" by Bill Watterson)
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Arturo Magidin
magidin-at-member-ams-org


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