Suzuki-Ree群的自同构群的阶分量刻画

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英文篇名：Automorphism Groups of Suzuki-Ree Groups Can Be Characterized by Their Order Components 作者：陈彦恒 ; 贾松芳 英文作者：Yan Heng CHEN;Song Fang JIA;School of Mathematics and Statistics, Chongqing Three Gorges University; 关键词：Suzuki-Ree群 ; 自同构群 ; 群的阶 ; 阶分量 英文关键词：Suzuki-Ree groups;;automorphism groups;;group order;;order component 中文刊名：SXXB 英文刊名：Acta Mathematica Sinica(Chinese Series) 机构：重庆三峡学院数学与统计学院; 出版日期：2019-07-15 出版单位：数学学报(中文版) 年：2019 期：v.62 基金：重庆市教委科研项目(KJ1710254);; 重庆三峡学院重大培育项目(18ZDPY07)及重点项目(14ZD16) 语种：中文; 页：SXXB201904010 页数：6 CN：04 ISSN：11-2038/O1 分类号：115-120

摘要

在《数学学报》2013年第56卷第4期中,"Suzuki-Ree群的自同构群的一个新刻画"一文证明了Aut(~2F_4(q)),q=2~f和Aut(~2G_2(q)),q=3~f,可由其阶分量刻画,其中f=3~s,s为正整数.本文证明了Aut(~2B_2(q)),q=2~f和Aut(2G2(q)),q=3~f,也可由其阶分量刻画,其中f为奇素数.结合二者得到结论:Suzuki-Ree单群的所有的素图不连通的自同构群皆可由其阶分量刻画.
        The paper[A new characterization of automorphism groups of Suzuki-Ree groups,Acta Math.Sin.,Chin.Ser., 2013,56(4),545-552]proved that Aut(~2 F_4(q)),q=2~f,and Aut(~2 G_2(q)),q=3~f,can be characterized by their order components,where f=3~s,s is a positive integer.We proved that Aut(~2 B_2(q)),q=2~f and Aut(~2 G_2(q)),q=3 f,also can be characterized by their order components,where f is a odd prime.Combining both,we can obtain that the automorphism groups of the Suzuki-Ree simple groups whose prime graphs are not connected can be characterized by their order components.

引文

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