Let H and K be normal subgroups of G such that H∩K = {e} and HK = G.

Prove that G ∼= H × K

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- Nov 18th 2009, 11:03 AMelninioNormal Subgroups
Let H and K be normal subgroups of G such that H∩K = {e} and HK = G.

Prove that G ∼= H × K - Nov 18th 2009, 11:07 AMaman_cc
- Nov 18th 2009, 11:08 AMtonio
- Nov 18th 2009, 06:31 PMelninio
Tonio, I'm not sure if this is the same thing as what you've posted but i've worked on this problem for over an hour and I know now that I can simply show that f is in isomorphism in a map defined f: H x K -> G by f((h,k)) = hk (Where hk is in G).

Does this seem correct so far? This is where I am having my trouble. I worked on one isomorphism problem similar to this before but I cant seem to apply any of the same methods or logic to this one.

How do I show f is an isomorphism in this problem? - Nov 18th 2009, 07:06 PMtonio