1. ## some questions about sylow thm and group action.

1. Let p be prime, and G be a finite group. If every element of G has order a power of p, then |G| = p^n for some n≥0. (Hint: Use Cauchy’s theorem.)

2. Tell as much as possible about the subgroups of a group of order 30 and of a group of order 40.

2. ## another emergent question

Let G be a finite p-group and H<G. Prove that H<NG(H).