Second Maximal Invariant Subgroups and Solubility of Finite Groups

被引：1

作者：

Shao, Changguo ^{[1
]}

Beltran, Antonio ^{[2
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing, Peoples R China

[2] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain

来源：

COMMUNICATIONS IN MATHEMATICS AND STATISTICS | 2024年 / 12卷 / 01期

关键词：

Invariant subgroups; Coprime action; Second maximal subgroup; Trivial intersection subgroup;

D O I：

10.1007/s40304-021-00279-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders. We prove that the fact of imposing specific properties on the second maximal A-invariant subgroups of G determines that G is either soluble or isomorphic to a few non-soluble groups such as PSL(2, 5) or SL(2, 5).

引用

页码：45 / 54

页数：10

共 50 条

[41] On δ-permutability of maximal subgroups of Sylow subgroups of finite groups
Qingjun Kong
Xiuyun Guo
Archiv der Mathematik, 2008, 91 : 106 - 110
[42] On δ-permutability of maximal subgroups of Sylow subgroups of finite groups
Kong, Qingjun
Guo, Xiuyun
ARCHIV DER MATHEMATIK, 2008, 91 (02) : 106 - 110
[43] The influence of second maximal subgroups on the generalized p-solvability of finite groups
Wang, Yuyun
Miao, Long
Gao, Zhichao
Liu, Wei
COMMUNICATIONS IN ALGEBRA, 2022, 50 (06) : 2584 - 2591
[44] GENERATING FINITE-GROUPS WITH MAXIMAL-SUBGROUPS OF MAXIMAL-SUBGROUPS
FLAVELL, P
JOURNAL OF ALGEBRA, 1995, 177 (02) : 372 - 384
[45] On nearly CAP-embedded second maximal subgroups of Sylow p-subgroups of finite groups
Zhang, Mingmei
Huang, Yuxi
Xu, Yong
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2024, (51): : 604 - 612
[46] Weak second maximal subgroups in solvable groups
Meng, Hangyang
Guo, Xiuyun
JOURNAL OF ALGEBRA, 2019, 517 : 112 - 118
[47] On Π-property of some maximal subgroups of Sylow subgroups of finite groups
Zhengtian Qiu
Jianjun Liu
Guiyun Chen
Czechoslovak Mathematical Journal, 2023, 73 : 1349 - 1358
[48] Finite groups with some maximal subgroups of Sylow subgroups ℳ-supplemented
Long Miao
Mathematical Notes, 2009, 86 : 655 - 664
[49] The finite subgroups of maximal arithmetic Kleinian groups
Chinburg, T
Friedman, E
ANNALES DE L INSTITUT FOURIER, 2000, 50 (06) : 1765 - +
[50] MAXIMAL-SUBGROUPS OF FINITE-GROUPS
ASCHBACHER, M
SCOTT, L
JOURNAL OF ALGEBRA, 1985, 92 (01) : 44 - 80

← 1 2 3 4 5 →