(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let M and N be normal subgroups of G, and suppose that the identity is the only element in both M and N. Prove that G is isomorphic to a subgroup of the product [itex]G/M\times G/N[/itex]

2. Relevant equations

Up until now, we've dealt with isomorphism, homomorphisms, automorphisms, Lagrange's Theorem, and other bits and pieces of theorems.

3. The attempt at a solution

I have no idea how to start this! I've looked over my notes and couldn't find anything obvious. I know that |M| divides |G| and the same goes for |N|. Does the fact that M and N only have {e} as a common element mean that |N| and |M| are relatively prime?

Also, can anybody explain exactly what, say, G/M is doing? My notes mention that it means "the cosets of M in G", but I'm not sure how to deal with it. Is there an official name for it so I can look up other information on it? Thanks!

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# Subgroup of a Direct Product

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