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具有两个p'维非线性不可约特征标的非可解群
引用本文:刘洋,鲁自群,张继平.具有两个p''维非线性不可约特征标的非可解群[J].数学年刊A辑(中文版),2020,41(1):039-52.
作者姓名:刘洋  鲁自群  张继平
作者单位:通信作者. 天津师范大学数学科学学院, 天津 300387.,清华大学数学科学系, 北京 100184.,北京大学北京国际数学研究中心, 北京 100871.
摘    要:McKay猜想是有限群表示理论中的一个重要问题.本文考虑了具有两个p'维不可约特征标的非可解群群G,并证明了McKay猜想对此类群成立.更进一步,当p为奇素数时,下面结果成立:p=3,G≌PSL_2(7)或存在一个正规2-群N,满足G/N≌PSL_2(5).

关 键 词:McKay  conjecture    Character  degrees    Nonsolvable  groups
收稿时间:2018/5/25 0:00:00

Nonsolvable Groups with Two Nonlinear Irreducible Characters of p'-Degrees
LIU Yang,LU Ziqun and ZHANG Jiping.Nonsolvable Groups with Two Nonlinear Irreducible Characters of p''-Degrees[J].Chinese Annals of Mathematics,2020,41(1):039-52.
Authors:LIU Yang  LU Ziqun and ZHANG Jiping
Institution:Corresponding author. School of Mathematical Science, Tianjin Normal University, Tianjin 300387, China.,Department of Mathematical Science, Tsinghua University, Beijing 100084, China. and BICMR, Peking University, Beijing 100871, China.
Abstract:McKay conjecture is an important problem in representation theory of finite groups. In this paper, the authors consider nonsolvable group with two $p''$-degree characters and prove the conjecture holds for such group. Furthermore, they show that if $G$ is a nonsolvable group such that $|\mathrm{Irr}_1(G,p'')|=2$ for odd prime $p$, then $p=3$, and $G\cong \mathrm{PSL}_2(7)$ or there exists a normal $2$-subgroup $N$ such that $G/N\cong \mathrm{PSL}_2(5)$.
Keywords:McKay conjecture  Character degrees  Nonsolvable groups
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