Finite groups with hall subnormally embedded Schmidt subgroups

被引：2

作者：

Monakhov, Victor S. ^{[1
]}

Kniahina, Viktoryia N. ^{[2
]}

机构：

[1] Gomel F Scorina State Univ, Dept Algebra & Geometry, Gomel, BELARUS

[2] Gomel F Scorina State Univ, Dept Fundamental & Appl Math, Gomel, BELARUS

来源：

COMMUNICATIONS IN ALGEBRA | 2020年 / 48卷 / 01期

关键词：

Derived subgroup; finite group; hall subgroup; nilpotent subgroup; subnormal subgroup;

D O I：

10.1080/00927872.2019.1632332

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A subgroup H of a finite group G is said to be Hall subnormally embedded in G if there is a subnormal subgroup N of G such that H is a Hall subgroup of N. A Schmidt group is a finite non-nilpotent group whose all proper subgroups are nilpotent. We prove the nilpotency of the second derived subgroup of a finite group in which each Schmidt subgroup is Hall subnormally embedded.

引用

页码：93 / 100

页数：8

共 50 条

[21] Finite groups with seminormal Schmidt subgroups
Knyagina, V. N.
Monakhov, V. S.
ALGEBRA AND LOGIC, 2007, 46 (04) : 244 - 249
[22] On finite groups with σ-subnormal Schmidt subgroups
Al-Sharo, Khaled A.
Skiba, Alexander N.
COMMUNICATIONS IN ALGEBRA, 2017, 45 (10) : 4158 - 4165
[23] Hall subgroups of finite groups
Revin, Danila Olegovitch
Vdovin, Evgenii Petrovitch
ISCHIA GROUP THEORY 2004, PROCEEDINGS, 2006, 402 : 229 - +
[24] Finite groups with Hall π-subgroups
Vedernikov, V. A.
SBORNIK MATHEMATICS, 2012, 203 (03) : 326 - 350
[25] ℱƬ-Embedded and ℱƬΦ-Embedded Subgroups of Finite Groups
X. Chen
W. Guo
A. N. Skiba
Algebra and Logic, 2015, 54 : 226 - 244
[26] Finite Groups with Generalized Subnormal Schmidt Subgroups
F. Sun
X. Yi
S. F. Kamornikov
Siberian Mathematical Journal, 2021, 62 : 364 - 369
[27] FINITE GROUPS WITH GENERALIZED SUBNORMAL SCHMIDT SUBGROUPS
Sun, F.
Yi, X.
Kamornikov, S. F.
SIBERIAN MATHEMATICAL JOURNAL, 2021, 62 (02) : 364 - 369
[28] Finite groups with a given set of Schmidt subgroups
Monakhov, VS
MATHEMATICAL NOTES, 1995, 58 (5-6) : 1183 - 1186
[29] On finite groups with generalized σ-subnormal Schmidt subgroups
Hu, Bin
Huang, Jianhong
COMMUNICATIONS IN ALGEBRA, 2018, 46 (07) : 3127 - 3134
[30] Finite supersolvable groups and Hall normally embedded subgroups of prime power order
Zheng, Weicheng
Meng, Wei
RICERCHE DI MATEMATICA, 2024,

← 1 2 3 4 5 →