最高阶元个数为6p^(2)q的有限群  

Finite Group With 6p^(2)q Elements of Maximal Order

作　　者：谭三标 艾海明[2] 晏燕雄[1] TAN San-biao;AI Hai-ming;YAN Yan-xiong(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;School of Science and Technology, Beijing Open University, Beijing 100081, China)

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]北京开放大学科学技术学院,北京100081

出　　处：《西南师范大学学报（自然科学版）》2021年第4期1-3,共3页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12071376,11971391);中央高校专项基金项目(XDJK2019C116,XDJK2019B030);西南大学教改项目(2018JY061).

摘　　要：众所周知,群的算术性质对群的结构有着很重要的影响.用群的各类数量性质刻画有限群的结构成为群论研究的热点问题.本文研究了最高阶元素的个数对有限群结构的影响,并证明了最高阶元素个数为6p^(2)q的有限群是可解群,其中p,q是素数,且q>p>13.It is well known that the arithmetic properties of a group have an important influence on the structure of the group.It has become a hot topic to describe the structure of a finite group by using the various quantitative properties of a group.In this article,the influence of the number of elements of maximal order of a finite group on the structure of such group has been studied.It is proved that finite groups with 6p^(2)q maximal order elements are solvable,where p,q are primes with q>p>13.

关 键 词：有限群 可解群 最高阶元的个数 Thompson猜想 

分 类 号：O152.1[理学—数学]