# Thread: Homomorphism 7

1. ## Homomorphism 7

If m is a homomorphism of G onto G' and N is a normal subgroup of G, show that m(N) is a normal subgroup of G'.

Please show steps, thanks!

2. Originally Posted by mpryal
If m is a homomorphism of G onto G' and N is a normal subgroup of G, show that m(N) is a normal subgroup of G'.

Please show steps, thanks!
I will give you a hint for this problem. In general if $m: G\to G'$ is a homorphism and $N$ is a normal subgroup of $G$ then $m(N)$ is a normal subgroup of $m(G)$. Prove this version. Then note if $m$ is onto then $m(G) = G$ and so $m(N)$ is a normal subgroup of $G$.

Show your work I do not want to help if you do not show your work.