Quotient groups and isomorphisms Let $H$ and $K$ be normal subgroups of $G$ such that $G = HK$.  Prove that $(G/H \cap K) \cong (G/H) \times (G/K)$.
To be honest, I'm not sure where to approach this.  I know that the statement that $H$ and $K$ are normal are to allow the quotient groups to occur.  I have studied the three isomorphic theorems and the correspondence theorem, but I do not really have a complete grasp on the concept.

Hint: Define a homomorphism $G\to (G/H)\times (G/K)$ in an obvious way. What is it's kernel?
