有限交换群的性质及推广  

Properties and Generalizations of Finite Exchange Groups

作　　者：姜琴 汪程[2] JIANG-Qin;WANG-Cheng(School of Mathematics and Computer Science,Hanjiang Normal University,Shiyan 442000,China;Yunyang Middle School,Shiyan 442000,China)

机构地区：[1]汉江师范学院数学与计算机科学学院,湖北十堰442000 [2]十堰市郧阳中学,湖北十堰442000

出　　处：《汉江师范学院学报》2024年第6期11-14,共4页Journal of Hanjiang Normal University

摘　　要：在已有结论的基础上分别讨论了有限交换群为素幂阶群、循环群所应具备的条件,及奇数阶可交换群、可交换单群的性质.同时也讨论了将可交换条件去掉,对于一个有限群分别构成正规子群、循环群及不构成单群所应具备的条件.Based on existing conclusions,this paper separately discusses the conditions that a finite abelian group must meet to be a simple power group or a cyclic group,as well as the properties of odd-order commutative groups and soluble single groups.It also examines the conditions for a finite group to form a normal subgroup,a cyclic group,or not to form a single group when the commutability condition is removed.

关 键 词：有限群 可交换 循环群 

分 类 号：O152.1[理学—数学]