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

共 50 条

[31] Finite groups with given nearly Sφ-embedded subgroups
Amjid, Venus
Cao, Chenchen
Mao, Yuemei
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (08)
[32] On S-permutably embedded subgroups of finite groups
Ballester-Bolinches, A.
Li, Yangming
MONATSHEFTE FUR MATHEMATIK, 2013, 172 (3-4): : 247 - 257
[33] Finite groups with sn-embedded or s-embedded subgroups
Malinowska, I. A.
ACTA MATHEMATICA HUNGARICA, 2012, 136 (1-2) : 76 - 89
[34] FINITE GROUPS WITH SOME SUBGROUPS OF SYLOW SUBGROUPS s*-SEMIPERMUTABLE
Kong, Qingjun
Guo, Xiuyun
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2021, 58 (02) : 147 - 156
[35] Semipermutable subgroups and s-semipermutable subgroups in finite groups
Li, Yangming
FRONTIERS OF MATHEMATICS IN CHINA, 2022, 17 (01) : 23 - 46
[36] Finite groups with some H-subgroups
Li, Xianhua
Zhao, Tao
Xu, Yong
INDAGATIONES MATHEMATICAE-NEW SERIES, 2011, 21 (1-2): : 106 - 111
[37] Finite groups with some weakly pronormal subgroups
Liu, Jianjun
Jiang, Mengling
Chen, Guiyun
OPEN MATHEMATICS, 2020, 18 : 1742 - 1747
[38] On some primary subgroups and the structure of finite groups
Kang, Ping
MONATSHEFTE FUR MATHEMATIK, 2014, 173 (04): : 519 - 527
[39] Finite groups with some SB-subgroups
Lu, Jiakuan
Zhang, Xueqin
Meng, Wei
Zhang, Boru
COMMUNICATIONS IN ALGEBRA, 2023, 51 (01) : 161 - 167
[40] Finite groups whose maximal subgroups have the hall property
Maslova N.V.
Revin D.O.
Siberian Advances in Mathematics, 2013, 23 (3) : 196 - 209

← 1 2 3 4 5 →