On the π-Quasinormality of 2-Maximal Subgroups of Sylow Subgroups of a Finite Group

被引：1

作者：

Chen, Songliang ^{[1
]}

Fan, Yun ^{[1
]}

机构：

[1] Cent China Normal Univ, Dept Math, Wuhan 430079, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2012年 / 19卷 / 04期

关键词：

pi-quasinormality; 2-maximal subgroup; p-nilpotency; ordered Sylow tower; supersolvability; SUFFICIENT CONDITIONS; MAXIMAL-SUBGROUPS;

D O I：

10.1142/S1005386712000521

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 a 2-maximal subgroup of G if there exists a maximal subgroup M of G such that H is a maximal subgroup of M. In this paper, we discuss the influence of pi-quasinormality of 2-maximal subgroups of Sylow subgroups on the structure of a finite group, and obtain some sufficient conditions under which the finite group is p-nilpotent, supersolvable, or possesses an ordered Sylow tower.

引用

页码：657 / 664

页数：8

共 50 条

[1] On ζs -Quasinormality of 2-Maximal Subgroups
Yufeng LIU
Xiaolong YU
Lijun HUO
[J]. Journal of Mathematical Research with Applications, 2013, (04) : 412 - 418
[2] INFLUENCE OF PI-QUASINORMALITY ON MAXIMAL-SUBGROUPS OF SYLOW SUBGROUPS OF FITTING SUBGROUP OF A FINITE-GROUP
ASAAD, M
RAMADAN, M
SHAALAN, A
[J]. ARCHIV DER MATHEMATIK, 1991, 56 (06) : 521 - 527
[3] On 2-maximal subgroups of finite groups
Konovalova, Marina N.
Monakhov, Victor S.
Sokhor, Irina L.
[J]. COMMUNICATIONS IN ALGEBRA, 2022, 50 (01) : 96 - 103
[4] Supersolubility of a Finite Group with Normally Embedded Maximal Subgroups in Sylow Subgroups
V. S. Monakhov
A. A. Trofimuk
[J]. Siberian Mathematical Journal, 2018, 59 : 922 - 930
[5] Supersolubility of a Finite Group with Normally Embedded Maximal Subgroups in Sylow Subgroups
Monakhov, V. S.
Trofimuk, A. A.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2018, 59 (05) : 922 - 930
[6] θ-Pairs for 2-maximal subgroups of finite groups
Feng, Haihui
Guo, Xiuyun
[J]. MONATSHEFTE FUR MATHEMATIK, 2009, 158 (04): : 393 - 401
[7] On maximal subgroups of Sylow subgroups of finite groups
Asaad, M
[J]. COMMUNICATIONS IN ALGEBRA, 1998, 26 (11) : 3647 - 3652
[8] θ-Pairs for 2-maximal subgroups of finite groups
Haihui Feng
Xiuyun Guo
[J]. Monatshefte für Mathematik, 2009, 158 : 393 - 401
[9] INFLUENCE OF NORMALITY ON MAXIMAL-SUBGROUPS OF SYLOW SUBGROUPS OF A FINITE-GROUP
RAMADAN, M
[J]. ACTA MATHEMATICA HUNGARICA, 1992, 59 (1-2) : 107 - 110
[10] On second maximal subgroups of Sylow subgroups of finite groups
Ballester-Bolinches, A.
Ezquerro, Luis M.
Skiba, Alexander N.
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2011, 215 (04) : 705 - 714

← 1 2 3 4 5 →