幂零群的若干等价条件  

Some Equivalent Conditions for Nilpotency of Finite Groups

作　　者：张勤海[1] 赵俊英[1] 

机构地区：[1]山西师范大学数学与计算机科学学院,山西临汾041004

出　　处：《西南师范大学学报（自然科学版）》2005年第1期26-30,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10171086);山西省自然科学基金资助项目(20011004);教育部重点科技项目资助项目(02023);山西省留学回国人员基金资助项目(晋出留管办字[2004]7号).

摘　　要：利用共轭置换子群的概念研究群的幂零性问题. 获得了一个群为幂零群的几个等价条件和若干充分条件.A subgroup H of a group G is called conjugate-permutable in G if it is permutable with every conjugate subgroup H^x of H for all x∈G. In this paper, the influnces of conjugate permutability on nilpotency of finite groups are investigated. Some equivalent and sufficient conditions for a group to be nilpotent are obtained.

关 键 词：共轭置换子群 内幂零群 幕零群 无不动点的自同构 

分 类 号：O152[理学—数学]