I've been solving the following problems from Herstein: " Given $N$ and $M$ normal in a group $G$, show that $NM/M$ is isomorphic to $N/N∩M$."
The problem is not difficult, but my doubt concerns the notation $NM/M$. Now I know that $G/N=(gN)$, where N is normal in G. But in $NM/M$ I would have $(nmM)=(nM)=N/M$. So Herstein wrote it like that as a subtle hint (in my proof I've constructed a homomorphism from $NM$ to $N/N∩M$ with kernel $M$) or am I wrong?