Normalizer property of finite groups with almost simple subgroups

被引：0

作者：

Hai, Jingjing ^{[1
]}

Ling, Xian ^{[2
]}

机构：

[1] Qingdao Univ, Coll Qual & Standardizat, Qingdao 266071, Peoples R China

[2] Qingdao Univ, Coll Math & Stat, Qingdao 266071, Peoples R China

来源：

ELECTRONIC RESEARCH ARCHIVE | 2022年 / 30卷 / 11期

关键词：

almost simple group; simple group; Coleman automorphism; q-central automorphism; normalizer property; COLEMAN AUTOMORPHISMS;

D O I：

10.3934/era.2022215

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove that all Coleman automorphisms of extension of an almost simple group by an abelian group or a simple group are inner. Using our methods we also show that the Coleman automorphisms of 2-power order of an odd order group by an almost simple group are inner. In particular, these groups have the normalizer property.

引用

页码：4232 / 4237

页数：6

共 50 条

[1] Carter subgroups of finite almost simple groups
E. P. Vdovin
[J]. Algebra and Logic, 2007, 46 : 90 - 119
[2] Carter subgroups of finite almost simple groups
Vdovin, E. P.
[J]. ALGEBRA AND LOGIC, 2007, 46 (02) : 90 - 119
[3] Groups with a finite number of normalizer subgroups
Tota, M
[J]. COMMUNICATIONS IN ALGEBRA, 2004, 32 (12) : 4667 - 4674
[4] The Normalizer Property for Finite Groups Whose Sylow 2-Subgroups are Abelian
Tao Zheng
Xiuyun Guo
[J]. Communications in Mathematics and Statistics, 2021, 9 : 87 - 99
[5] The Normalizer Property for Finite Groups Whose Sylow 2-Subgroups are Abelian
Zheng, Tao
Guo, Xiuyun
[J]. COMMUNICATIONS IN MATHEMATICS AND STATISTICS, 2021, 9 (01) : 87 - 99
[6] GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS
Lucchini, Andrea
Marion, Claude
Tracey, Gareth
[J]. FORUM OF MATHEMATICS SIGMA, 2020, 8
[7] Maximal subgroups of small index of finite almost simple groups
Ballester-Bolinches, Adolfo
Esteban-Romero, Ramon
Jimenez-Seral, Paz
[J]. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2022, 116 (04)
[8] On factorization of finite almost simple groups by nonconjugate maximal subgroups
Tikhonenko, T. V.
Tyutyanov, V. N.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2010, 51 (01) : 174 - 177
[9] Maximal subgroups of small index of finite almost simple groups
Adolfo Ballester-Bolinches
Ramón Esteban-Romero
Paz Jiménez-Seral
[J]. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2022, 116
[10] On factorization of finite almost simple groups by nonconjugate maximal subgroups
T. V. Tikhonenko
V. N. Tyutyanov
[J]. Siberian Mathematical Journal, 2010, 51 : 174 - 177

← 1 2 3 4 5 →