Let $G$ be a group and $N'=[N,N]$ the commutator subgroup of $N$. How do I show that If $N\lhd G$ and $N$ and $\frac{G}{N'}$ are nilpotent, then $G$ is nilpotent.
Prove: If $N\lhd G$ and $N$ and $\frac{G}{N'}$ are nilpotent, then $G$ is nilpotent.
12
$\begingroup$
group-theory