I'm having trouble with an exercise in "Introduce to the theory of group" book. This is problem:
Let $M$ be a maximal subgroup of $G$. Prove that if $M$ is a normal subgroup of $G$, then $[G: M]$ is finite and equal to a prime.
I'm having trouble with an exercise in "Introduce to the theory of group" book. This is problem:
Let $M$ be a maximal subgroup of $G$. Prove that if $M$ is a normal subgroup of $G$, then $[G: M]$ is finite and equal to a prime.