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December 10th, 2008, 07:51 AM   #1
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please help quickly about sylow thm and group action quest

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.



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



please help me quickly... ? dont understand these ques.s
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December 13th, 2008, 06:13 AM   #2
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Re: please help quickly about sylow thm and group action quest

For problem (1), try a proof by contradiction.
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