具有两个特殊特征标维数的有限群  

Finite Groups with Exactly Two Special Character Degrees

作　　者：陈小莉 吕恒[1] CHEN Xiaoli;LÜHeng(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10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(11971391,12071376);重庆市科学创新项目(CYB20087).

摘　　要：本文通过有限单群分类定理,首先证明了非交换单群S至少存在3个维数不同的不可约特征标χ,使得χ(1)2■|S|.设G为有限群,且只有两个不可约特征标χ满足χ(1)2■|G∶kerχ|,则G非单,进一步证明了G为可解群.In this paper,by means of the classification theorem of finite simple groups,it is proved that there are at least three irreducible charactersχof nonabelian simple group S with different dimension which satisfy thatχ(1)2|S|.Let G be a finite group with two irreducible characters which satisfy thatχ(1)2|G∶kerχ|,then G is a non-simple group,and it is further proved that G is a solvable group.

关 键 词：有限群 不可约特征标 维数 余维数 

分 类 号：O152.1[理学—数学]