Refer to Lang's Algebra problem 14b, Chapter 1, p.76.
Let $G$ be a finite group and $N$ normal in $G$ such that the order of $N$ and its index in $G$ are relatively prime. Let $g$ be an automorphism of $G$. Then $g(N)=N$.
Any hints?
Refer to Lang's Algebra problem 14b, Chapter 1, p.76.
Let $G$ be a finite group and $N$ normal in $G$ such that the order of $N$ and its index in $G$ are relatively prime. Let $g$ be an automorphism of $G$. Then $g(N)=N$.
Any hints?