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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.
--
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"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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