循环群的一个新的特征性质(英文)

A NEW CHARACTERISTIC PROPERTY OF A CYCLIC GROUP

Two characteristic properties of a cyclic group are given: 1~0A group G is cyclic if and only every subgroup of G is G^mwhere G^m={X^n|X∈G}and m is a integer. See,[1] 2~0 A group G is cyclic if and only if the index of every subgroupof G is finite and for every positive integer k,in G at most thereexists a subgroup H having index k. See,[2]