一类共轭类长度集合的长度为3的有限群  

A Type of Finite Groups With Three Conjugacy Lengths

作　　者：曹熠维 吕恒[1] CAO Yi-wei;Lü Heng(School of Mathematics and Statistics,Southwest University,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2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(11971391).

摘　　要：证明了:若G为有限群,且|cd(G)|=|cs(G)|=3,则G=H×A.其中A是交换群,H是非交换p-群且|cs(H)|=3,或H=KL,K■H,(|K|,|L|)=1,K是非交换p-群且|cs(K)|=2,L是交换群,Z(K)=Z(H)∩K,H/Z(H)是Frobenius群,并且|cd(K)|=2,c(K)=2.This paper is based on the classification of finite groups with three conjugacy lengths to find out which have three character degrees.If G is a finite group with three conjugacy lengths and three character degrees,then G=H×A,H is an unabelian p-group,A is abelion;or H=KL,K■H,(|K|,|L|)=1,K is an unabelian p-group with two conjugacy lengths and L is abelian,Z(K)=Z(H)∩K,H/Z(H)is a Frobenius group,and K have two different character degrees,the nilpotent class of K is two.

关 键 词：有限群 共轭类长度 特征标维数 

分 类 号：O152.1[理学—基础数学]