最高阶元素个数为4p^2的有限群是可解群  

Finite Groups with |M(G)|=4p^2 Elements of Maximal Order Are Solvable

作　　者：晏燕雄[1,2] 

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]重庆第二师范学院数学与信息工程系,重庆400067

出　　处：《河南师范大学学报（自然科学版）》2012年第4期5-8,共4页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11171364);重庆市科委自然科学基金(cstc2011jjA1495);重庆市教委资助项目(KJ110609)

摘　　要：研究了最高阶元素个数对有限群结构的影响.运用群阶的素因子,k阶循环子群共轭类的长,以及K3-单群和K4-单群的有关结论,证明了最高阶元素个数为|M(G)|=4p2的有限群G是可解群,其中p是素数.Affection on the structure of finite group as the number of maximal order elements is discussed. It is proved that such finite groups with 4p2 maximal order elements are solvable by making use of corresponding results on K3-simple groups and K4-simple groups, as well as the prime factor of the order of a finite group and the length of the conjugate class of cyclic subgroups with order k, where p is a prime

关 键 词：有限群 可解群 元素的阶 m-型 

分 类 号：O152.1[理学—数学]