| 贾松芳,陈彦恒.Artin单群的一种刻画[J].数学年刊A辑,2020,41(3):325~330 |
| Artin单群的一种刻画 |
| A Characterization of Artin Simple Groups |
| Received:May 13, 2018 Revised:May 11, 2020 |
| DOI：10.16205/j.cnki.cama.2020.0023 |
| 中文关键词: 有限群, Artin单群, 群阶, 共轭类长 |
| 英文关键词:Finte group, Artin simple groups, Group order, Conjugacy class length |
| 基金项目:重庆市教委科学技术研究项目 (No.KJ1710254, No.KJQN202001217) 和重庆三峡学院重大培育项目 (No.18ZDPY07) |
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| 中文摘要: |
| 设 L 是一个有限单群. 若存在素数 p, 使得 p mid |L| 且 p>|L|^{frac{1}{3}},则称 L 是一个Artin单群. Brauer和Reynolds在1958年给出了Artin单群的完全分类:PSL_2(p), p>3 是一个素数, 和 PSL_2(p-1), p>3 为一个Fermat素数.不借助于有限单群分类定理, 本文利用群阶和一个共轭类长刻画了Artin单群, 作为推论得出了Thompson猜想对Artin单群成立. |
| 英文摘要: |
| Let L be a finite simple group. If it exists a prime p such that p | |L| and p > |L| 13 , then L is called an Artin simple group. In 1958, Brauer and Reynolds classified Artin simple groups, which are P SL2(p) where p > 3 is a prime, and P SL2(p 1) where p > 3 is a Fermat prime. Without the help of classification theorem of finite simple groups,the authors characterize the Artin simple groups by their order and one conjugacy class length in this short note. This work implies that Thompson’s conjecture holds for Artin simple groups. |
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