Recent content by Avatarjoe

Homework Statement We've shown if G_{1},G_{2},...,G_{n} are subgroups of G s.t. 1)G_{1},G_{2},...,G_{n} are all normal 2)Every element of G can be written as g_{1}g_{2}...g_{n} with g_{i}\inG 3)For 1\leqi\leqn, G_{i}\capG_{1},G_{2},...,G_{i-1}=e then G\congG_{1}xG_{2}x...xG_{n}...

Right. Thanks, that is what I meant. So g↦ (Hg, Kg) is a homomorphism and that's easy to prove. Also H∩K will be the kernal. If I'm not mistaken, I just need to show that {Hg x Kg} is a subgroup of G/H x G/K and then the homomorphism will be onto that subgroup by the way I defined it. Then...

Homework Statement Suppose H and K are normal subgroups of G. Prove that G/H x G/K has a subgroup isomorphic to G/(H\capK) Homework Equations The Attempt at a Solution I was trying to find a homomorphism from G to G/H x G/K where G/(H\capK) is the kernal. Maybe something like if g is in H it...