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

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