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Subgroup proof

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Prove: any subgroup of the order of p^(n-1) in a group of order p^n, where p is a prime, is a normal subgroup

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This is a proof regarding normal groups

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Proof: Suppose G is a group with order |G|=p^n. H is a subgroup of G with order |H|=p^(n-1). p is a prime. Now we show that H is a normal subgroup.
We consider N(H)={x|x ...

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