Possible Duplicate:
Proof of first isomorphism theorem of group
Let $G_1, G_2$ be groups. If $f: G_1 \rightarrow G_2$ is a group homomorphism with $K = \ker(f)$, then $G_1 / K$ is isomorphic to $f(G_1)$.
This was a theorem in the book that was left unproven and I'm really curious as to how you would go about it.