| 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,2020,41(1):039~52 |
| 具有两个p'维非线性不可约特征标的非可解群 |
| Nonsolvable Groups with Two Nonlinear Irreducible Characters of p'-Degrees |
| Received:May 25, 2018 |
| DOI：10.16205/j.cnki.cama.2020.0003 |
| 中文关键词: McKay conjecture, Character degrees, Nonsolvable groups |
| 英文关键词:McKay conjecture, Character degrees, Nonsolvable groups |
| 基金项目: |
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| 中文摘要: |
| 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: $p=3$, $G\cong \mathrm{PSL}_2(7)$或存在一个正规$2${-}群$N$, 满足 $G/N\cong \mathrm{PSL}_2(5)$. |
| 英文摘要: |
| 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 $G/N\cong \mathrm{PSL}_2(5)$. |
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