关于循环群和交换群的等价刻画  

Equivalent characterizations of cyclic groups and abelian groups

作　　者：史江涛[1] 毕凌霄 李娜 SHI Jiang-tao;BI Ling-xiao;LI Na(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院

出　　处：《云南民族大学学报（自然科学版）》2019年第6期563-565,共3页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(11561021;11761079);山东省自然科学基金(ZR2017MA022);烟台大学研究生教育创新计划(120202)资助项目

摘　　要：考虑某些交换子群具有特殊的正规化子,用初等方法证明了循环群和交换群的等价刻画:设G为有限群,则G是循环群当且仅当G的每个极小子群的正规化子皆是循环群;G是交换群当且仅当G的每个初等交换子群的正规化子皆是交换群.Considering some abelian subgroups with special normalizers,we have proved the following equivalent characterizations of cyclic groups and abelian groups by elementary methods:Let G be a finite group;then G is a cyclic group if and only if the normalizer of every minimal subgroup of G is a cyclic group;G is an abelian group if and only if the normalizer of every elementary abelian subgroup of G is an abelian group.

关 键 词：循环群 交换群 极小子群 初等交换子群 正规化子 

分 类 号：O152.1[理学—数学]