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单词 ProofThatEveryGroupOfPrimeOrderIsCyclic
释义

proof that every group of prime order is cyclic


The following is a proof that every group of prime order is cyclic.

Let p be a prime and G be a group such that |G|=p. Then G contains more than one element. Let gG such that geG. Then g contains more than one element. Since gG, by Lagrange’s theorem, |g| divides p. Since |g|>1 and |g| divides a prime, |g|=p=|G|. Hence, g=G. It follows that G is cyclic.

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