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 $\displaystyle m: G\to G'$ is a homorphism and $\displaystyle N$ is a normal subgroup of $\displaystyle G$ then $\displaystyle m(N)$ is a normal subgroup of $\displaystyle m(G)$. Prove this version. Then note if $\displaystyle m$ is onto then $\displaystyle m(G) = G$ and so $\displaystyle m(N)$ is a normal subgroup of $\displaystyle G$.
Show your work I do not want to help if you do not show your work.