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