Let $N $ be a normal subgroup of order $p$ contained in a group $G$ of order $p^n$. Here $p$ is a prime number. Then I have to show thst $N$ is in the center of $G$.
This is an exercise 15 in p.92 of Hungerford.
I thought of acting $G$ on $N$ but cannot find a way through.
Could anyone please help me?