On finite groups with Hall normally embedded Schmidt subgroups

被引：0

作者：

Kniahina, Viktoryia N. ^{[1
]}

Monakhov, Victor S. ^{[1
]}

机构：

[1] Francisk Skorina Gomel State Univ, Dept Math, Sovetskaya Str 104, Gomel 246019, BELARUS

来源：

ALGEBRA & DISCRETE MATHEMATICS | 2018年 / 26卷 / 01期

关键词：

finite group; Hall subgroup; normal subgroup; derived subgroup; nilpotent subgroup;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A subgroup H of a finite group G is said to be Hall normally embedded in G if there is a normal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a non-nilpotent finite group whose all proper subgroups are nilpotent. In this paper, we prove that if each Schmidt subgroup of a finite group G is Hall normally embedded in G, then the derived subgroup of G is nilpotent.

引用

页码：90 / 96

页数：7

共 50 条

[21] On normally embedded subgroups of a finite group
Shen, Zhencai
Chen, Yingyi
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2014, 13 (07)
[22] Finite groups with subnormal Schmidt subgroups
V. A. Vedernikov
Algebra and Logic, 2007, 46 : 363 - 372
[23] Finite Groups with σ-Subnormal Schmidt Subgroups
Ballester-Bolinches, A.
Kamornikov, S. F.
Yi, X.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2022, 45 (05) : 2431 - 2440
[24] Finite Groups with Subnormal Schmidt Subgroups
V. N. Knyagina
V. S. Monakhov
Siberian Mathematical Journal, 2004, 45 : 1075 - 1079
[25] Finite groups with subnormal Schmidt subgroups
Knyagina, VN
Monakhov, VS
SIBERIAN MATHEMATICAL JOURNAL, 2004, 45 (06) : 1075 - 1079
[26] Finite groups with σ-subnormal Schmidt subgroups
Yi, Xiaolan
Kamornikov, S. F.
JOURNAL OF ALGEBRA, 2020, 560 : 181 - 191
[27] Finite groups with seminormal Schmidt subgroups
V. N. Knyagina
V. S. Monakhov
Algebra and Logic, 2007, 46 : 244 - 249
[28] Finite groups with subnormal Schmidt subgroups
Vedernikov, V. A.
ALGEBRA AND LOGIC, 2007, 46 (06) : 363 - 372
[29] Finite groups with seminormal Schmidt subgroups
Knyagina, V. N.
Monakhov, V. S.
ALGEBRA AND LOGIC, 2007, 46 (04) : 244 - 249
[30] On finite groups with σ-subnormal Schmidt subgroups
Al-Sharo, Khaled A.
Skiba, Alexander N.
COMMUNICATIONS IN ALGEBRA, 2017, 45 (10) : 4158 - 4165

← 1 2 3 4 5 →