1. ## normal subgroup, homomorphism

Suppose $f: G \rightarrow H$ is a group homomorphism, $N \triangleleft G$, and $\text{ker}(f) \leq N$.

Prove that
$G/N \cong f(G)/f(N)$.

I don't see how to do this. Any hints would be nice. Thank you.

2. Originally Posted by maya8913
Suppose $f: G \rightarrow H$ is a group homomorphism, $N \triangleleft G$, and $\text{ker}(f) \leq N$.

Prove that
$G/N \cong f(G)/f(N)$.

I don't see how to do this. Any hints would be nice. Thank you.
use the fact that $f(G)/f(N)=(G/\ker f)/(N/\ker f)=G/N$