[1]贾松芳,陈彦恒,姜友谊.Ree群 2G2(q)自同构群阶分量刻画的简化证明[J].四川师范大学学报(自然科学版),2020,43(03):333-336.[doi:10.3969/j.issn.1001-8395.2020.03.007]
 JIA Songfang,CHEN Yanheng,JIANG Youyi.The Simplified Proof for Order Components Characterization of the Automorphism of Ree Group 2G2(q)[J].Journal of SichuanNormal University,2020,43(03):333-336.[doi:10.3969/j.issn.1001-8395.2020.03.007]
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Ree群 2G2(q)自同构群阶分量刻画的简化证明()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年03期
页码:
333-336
栏目:
基础理论
出版日期:
2020-05-05

文章信息/Info

Title:
The Simplified Proof for Order Components Characterization of the Automorphism of Ree Group 2G2(q)
文章编号:
1001-8395(2020)03-0333-04
作者:
贾松芳 陈彦恒 姜友谊
重庆三峡学院 数学与统计学院, 重庆 万州 404100
Author(s):
JIA Songfang CHEN Yanheng JIANG Youyi
School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100
关键词:
有限单群 Sylow 2-子群 自同构群 阶分量
Keywords:
finite simple groups Sylow 2-subgroup automorphism group order components
分类号:
O152.1
DOI:
10.3969/j.issn.1001-8395.2020.03.007
文献标志码:
A
摘要:
借助Sylow 2-子群阶数≤8的有限单群的分类,证明Ree群2G2(q)(q=33s,s≥1)的自同构群可被其阶分量刻画,简化文献(肖芳芳,曹洪平,陈贵云.数学学报,2013,56(4):545-552.)中命题3的证明.
Abstract:
In this short paper, on basis of the classification of finite simple groups whose Sylow 2-subgroups' order are no more than 8, we prove that the automorphism of Ree group2G2(q)can be characterized by its order components, which simplifies the proof of Proposition 3 of(Xiao F F, Cao H P, Chen G Y. Acta Mathematica Sinica,2013,56(4):545-552.).

参考文献/References:

[1] WILLIAMS J S. Prime graph components of finite groups[J]. J Algebra,1981,69(2):487-513.
[2] 陈贵云. 李型单群2G2(q)的新刻画[C]//中国科技技术协会第二届青年学术年会四川卫星会议论文集. 成都:西南交通大学出版社,1995:221-224.
[3] KHUKHRO E I, MAZUROV V D. Unsolved Problems in Group Theory:the Kourovka Notebook[M]. 17th ed. Novosibirsk:Sobolev Institute of Mathematics,2010.
[4] CHEN G Y. On Thompson's conjecture[J]. J Algebra,1996,185(1):184-193.
[5] CHEN G Y. A new characterization of sporadic simple groups[J]. Algebra Colloq,1996,3(1):49-58.
[6] CHEN G Y. A new characterization of sporadic simple groups[J]. Chinese Science Bulletin,1996,41(8):702-703.
[7] CHEN G Y. A new characterization of Suzuki-Ree groups[J]. Science in China,1996,A40(8):807-812.
[8] 陈贵云. G2(q),q≡0(mod 3)的新刻划[J]. 西南师范大学学报(自然科学版),1996,21(3):47-51.
[9] 陈贵云. 李型单群G2(q)的阶分量刻画[J]. 西南师范大学学报(自然科学版),2001,26(5):42-48.
[10] CHEN G Y. Characterization of 3D4(q)[J]. Southeast Asian Bulletin of Math,2001,25(3):389-401.
[11] IRANMANESH A, ALAVI S H. A characterization of F4(q) where q is even[J]. J Math Sci,2000,2(6):853-859.
[12] IRANMANESH A, ALAVI S H. A characterization of simple groups L5(q)[J]. Bull Austral Math Soc,2002,65(2):211-222.
[13] IRANMANESH A, ALAVI S H. A characterization of C2(q) where q>5 is even[J]. Comment Math Univ Carolinae,2002,43(1):9-21.
[14] IRANMANESH A, ALAVI S H, KHOSRAVI B. A characterization of L3(q) where q is an odd prime power[J]. J Pure and Applied Algebra,2002,170(2/3):243-254.
[15] IRANMANESH A, ALAVI S H, KHOSRAVI B. A characterization of L3(q) for q=2n[J]. Acta Mathematica Sinica(English Series),2002,18(3):463-472.
[16] BEHROOZ K, BAHMAN K. A characterization of E6(q)[J]. Algebra Groups and Geometries,2002,19(2):225-243.
[17] IRANMANESH A, ALAVI S H. A characterization of U5(q) for q=2n[J]. Internatioanl Mathematical J,2003,3(2):129-141.
[18] BEHROOZ K, BAHMAN K. A characterization of 2E6(q)[J]. Kumamoto J Math,2003,16:1-11.
[19] CHEN G Y, SHI H G. 2Dp(3)(9≤p=2m-1 not a prime)can be characterized by its order component[J]. J Appl Math Computing,2005,19(1/2):353-362.
[20] SHI H G, CHEN G Y. 2Dp+1(2)(5≤p≠2m-1)can be characterized by its order component[J]. Kumamoto J Math,2005,18:1-8.
[21] 肖芳芳,曹洪平,陈贵云. Suzuki-Ree群的自同构群的一个新刻画[J]. 数学学报,2013,56(4):545-552.
[22] MONGHADDAMFAR A R, ZOKAYI A R, DARAFSHEH M R. A characterization of finite simple groups by the degrees of vertices of their prime graphs[J]. Algebra Colloq,2005,12(3):431-442.
[23] CONWAY J H, CURTIS R T, NORTON S P, et al. Atlas of Finite Groups[M]. Oxford:Clarendon Press,1985.
[24] 徐明耀. 有限群导引(上)[M]. 北京:科学出版社,1993.
[25] 陈贵云. Frobenius 群与2-Frobenius群的结构[J]. 西南师范大学学报(自然科学版),1995,20(5):485-487.
[26] IIYORI N, YAMAKI H. Prime graph components of the simple groups of Lie type over the field of even charateristic[J]. J Algebra,1993,155(2):335-343.
[27] KONDRATÉV A S. On prime graph components of finite simple groups[J]. Mathematics of the USSR-Sbornik,1990,180(6):787-797.
[28] LUCIDO M S. Prime graph components of finite almost simple groups[J]. Rend Sem Univ Padova,1999,102:1-22.

备注/Memo

备注/Memo:
收稿日期:2018-10-15 接受日期:2018-11-07 基金项目:重庆市科委研究项目(CSTC2014JCYJA00009)和重庆市教委科研项目(KJ1710254) 第一作者简介:贾松芳(1980-),女,讲师,主要从事有限群的研究,E-mail:jiasongfang@163.com
更新日期/Last Update: 2020-05-05