I'm trying to prove that if M,N are normal in G and MN = G, then [tex]G/(M\cap N)\cong G/M \times G/N[/tex] In an attempt to use the 1st Isom. Thm, I have a homomorphism from G to G/M x G/N : [tex]g \mapsto (gM, gN)[/tex] The kernel is [tex]M\cap N[/tex], so I just have to show that the function is onto to get the isomorphism. My guess is that (aM, bN) = (abM, abN). I am having a difficult time showing this, or I may be wrong. Any help?