一类阶为2pqr的CA-群  

A Kind of CA-Groups of Order 2pqr

作　　者：陈佳琪 周伟[1] CHEN Jiaqi;ZHOU Wei(School of Mathematics and Statistics, Southwest Universitiy, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2021年第12期1-4,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971391).

摘　　要：如果对任意x∈G\Z(G),有CG(x)交换,则称群G为CA-群.通过反证法,证明了阶为2pqr的群是CA-群,其中p,q,r均为素数,且2<p<q<r,r-12<p.If CG(x)is commutative for any x∈G\Z(G),then the group G is called CA-group.It is proved in this paper that a group of order 2pqr is a CA-group by using reduction to absurdity,where p,q,r are all primes,2<p<q<r and r-12<p.

关 键 词：中心化子 正规化子 SYLOW子群 直积 

分 类 号：O152.1[理学—数学]