最高阶元素个数为4p^m的有限群  

FINITE GROUPS HAVING 4p^m ELEMENTS OF MAXIMAL ORDER

作　　者：姜友谊[1] 苏翃[2] 王绍恒[1] 

机构地区：[1]重庆三峡学院数学系,重庆万州404000 [2]重庆工学院数理学院,重庆400050

出　　处：《数学杂志》2007年第2期191-194,共4页Journal of Mathematics

基　　金：重庆市教委科技计划项目(KJ061102);重庆市科委科技攻关项目(CSTC2005EA7029)

摘　　要：本文研究了最高阶元素个数对群结构的影响.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-单群的相关结论,证明了最高阶元素个数为4pm(p为素数,p>17,2p+1≠2a3b-1,且2a3b-1是素数,m是正整数)的有限群是可解群.Affection on the structure of finite group as the number of maximal order elements is discussed. It is proved that such finite groups with 4pm maximal order elements are solvable by making use of corresponding results on K3-simple group and K4-simple group, as well as the prime factor of the order of a group and the length of the conjugate class of cyclic subgroups with order k. where p is prime with p〉17,2p＋1≠2^a3^b,且2^a3^b-1 is prime and m is a positive integer.

关 键 词：可解群 最高阶元 共轭类的长 单群 素因子 

分 类 号：O152.1[理学—数学]