(Theorem) If $G$ is a simple group of odd order , then $G \cong \mathbb Z_p$ for some prime $p$.

Question

I am studying Dumit Foote. I have seen this result in this book. Please help me solve this.

Thank you.

Answer 1

It is easy to see that the theorem in the title is equivalent to the Feit-Thompson theorem, which states that every finite group of odd order is solvable. Proving the theorem is very difficult, the original proof was about 200 pages long.