| 具有两个p'维非线性不可约特征标的非可解群 |
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| 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 |
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| 作者姓名： | 刘洋 鲁自群 张继平 |
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| 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. |
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| 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).
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| 关 键 词： | McKay conjecture Character degrees Nonsolvable groups |
| 收稿时间： | 2018-05-25 |
Nonsolvable Groups with Two Nonlinear Irreducible Characters of p'-Degrees |
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| 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 |
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| Authors: | LIU Yang LU Ziqun ZHANG Jiping |
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| Affiliation: | 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. |
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| Abstract: | McKay conjecture is an important problem in representation theory offinite groups. In this paper, the authors consider nonsolvable groupwith two $p''$-degree characters and prove the conjecture holds forsuch group. Furthermore, they show that if $G$ is a nonsolvablegroup such that $|mathrm{Irr}_1(G,p'')|=2$ for odd prime $p$, then$p=3$, and $Gcong mathrm{PSL}_2(7)$ or there exists a normal$2$-subgroup $N$ such that $G/Ncong mathrm{PSL}_2(5)$. |
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| Keywords: | McKay conjecture Character degrees Nonsolvable groups |
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