We're learning normal subgroups, kernels, homomorphisms and isomorphisms in abstract algebra right now. I'm trying to tie the ends together:
I know that if $G$ is a group, $N$ a normal subgroup of $G$, and $\phi: G\to G′$ is a homomorphism then $\phi(N)$ is a normal subgroup of $G′$.
But can I say that quotient group $G/N$ is isomorphic to $G'/ \phi(N)$?
Let's assume that $\phi$ is a surjective homomorphism.