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Unformatted text preview: H G be a subgroup of order 24. Suppose that there is at least one left coset of H in G (other than H itself) that is also a right coset of H in G . Prove that H is a normal subgroup of G . 4 4. Let G be a group and let H be a subgroup of G such that the index ( G : H ) is nite. Prove that there is a normal subgroup H of G such that H H and such that ( G : H ) is nite. Show further that there is an n 1 so that g n H for all g G . 5 5. Let G be a nite group, and let H be a normal subgroup of G . Let P be a pSylow subgroup of H , and let K be the normalizer of P in G . Establish the equality G = HK . 6...
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 Spring '10
 tao/analysis
 Math

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