关于有限群的循环子群的注记

A Note on Cyclic Subgroups of Finite Groups

利用循环子群之外的元素的阶和该循环子群的阶的关系给出了关于循环群的一个刻画;刻画了导子群G′的每个极小子群或者正规或者具有循环正规化子的有限群G,并证明了这类群G是可解的。

We give a characterization of cyclic group by using the relation between the order of the elements outside the cyclic subgroup and the order of the cyclic subgroup.We also characterize the finite group G,in which every minimal subgroup of its derived subgroup G′is normal or has cyclic normalizer,and prove that such a group G is solvable.