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Let $M$ and $N$ be normal subgroups of $G$ s.t. $G=MN$. Prove that $G/(M\cap N)\cong (G/M)\times (G/N)$.

I have got the proof. But the question asks to draw the lattice. Is there any lattice? Since we don't know what's the groups $M$, $N$ and $G$ are like.

What's the lattice?

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1 Answer 1

I think one means the 4-element lattice $\{M,N,\inf(M,N)=M\cap N, \sup(M,N)=MN=G\}$.

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@ Babak S.: Dear Babak S., sorry, I don't English well so I don't understand your comment. – Boris Novikov Apr 4 '13 at 8:17

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