On finite groups with some Hall normally embedded subgroups

被引：2

作者：

Meng, Wei ^{[1
,2
]}

Lu, Jiakuan ^{[3
]}

机构：

[1] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541002, Guangxi, Peoples R China

[2] Southern Univ Sci & Technol, SUSTech Int Ctr Math, Shenzhen 518055, Guangdong, Peoples R China

[3] Guangxi Normal Univ, Sch Math & Stat, Guilin 541004, Guangxi, Peoples R China

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2025年 / 24卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Hall normally embedded; minimal subgroup; maximal subgroup; solvable group; MINIMAL SUBGROUPS;

D O I：

10.1142/S0219498825501907

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a finite group. A subgroup H of G is called Hall normally embedded in G if H is a Hall subgroup of HG, where HG is the normal closure of H in G, that is, the smallest normal subgroup of G containing H. A group G is called a PHN-group if its all minimal subgroups and cyclic subgroup of order 4 are Hall normally embedded in G. In this paper, we give the classification of minimal non-PHN-groups. Furthermore, we investigate the structure of finite group all of whose maximal subgroups of even order are PHN-groups.

引用

页数：15

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