We use elementary method to prove the following result,which generalizes the Exercise 3 in Sec-tion 1.4 of[1].Let G be a finite group and p the smallest prime divisor of|G|.If for any positive integer n dividing|G|we always have|{x∈G|xn=1}|≤(p-1)n,then G is a cyclic group.
关键词
有限群/最小素因子/素数幂阶子群/正规/循环群
Key words
finite group/the smallest prime divisor/subgroup of prime-power order/normal/cyclic group
维普
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