FINITE GROUPS WITH HEREDITARILY G-PERMUTABLE SCHMIDT SUBGROUPS

被引：3

作者：

Ballester-Bolinches, A. ^{[1
]}

Kamornikov, S. F. ^{[2
]}

Perez-calabuig, V. ^{[3
]}

Tyutyanov, V. N. ^{[4
]}

机构：

[1] Guangdong Univ Educ, Dept Math, Guangzhou 510303, Guangdong, Peoples R China

[2] Francisk Skorina State Gomel Univ, Gomel, BELARUS

[3] Univ Valencia, Dept Matemat, Dr Moliner 50, Valencia 46100, Spain

[4] Int Univ MITSO, Gomel Branch, Gomel, BELARUS

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2024年 / 109卷 / 03期

关键词：

finite group; Schmidt subgroup; hereditarily G-permutable subgroup;

D O I：

10.1017/S0004972723000771

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A subgroup A of a group G is said to be hereditarily G-permutable with a subgroup B of G, if AB(x) = B(x)A for some element x is an element of < A,B >. A subgroup A of a group G is said to be hereditarily G-permutable in G if A is hereditarily G-permutable with every subgroup of G. In this paper, we investigate the structure of a finite group G with all its Schmidt subgroups hereditarily G-permutable.

引用

页码：522 / 528

页数：7

共 10 条

[1]

Ballester-Bolinches A, 2022, B MALAYS MATH SCI SO, V45, P2431, DOI 10.1007/s40840-022-01369-y

[2]

Ballester-Bolinches A., 2023, MED J MATH, V20, P1

[3]

Ballester-Bolinches A., 2006, Classes of finite groups, Mathematics and its Applications

[4]

DOERK K., 1992, FINITE SOLUBLE GROUP, DOI DOI 10.1515/9783110870138

[5]

Golfand J.A., 1948, DOKL AKAD NAUK+, V60, P1313

[6] X-quasinormal subgroups [J].

Guo, W. ;

Skiba, A. N. ;

Shum, K. P. .

SIBERIAN MATHEMATICAL JOURNAL, 2007, 48 (04) :593-605

[7] Finite groups with a given set of Schmidt subgroups [J].

Monakhov, VS .

MATHEMATICAL NOTES, 1995, 58 (5-6) :1183-1186

[8]

Schmidt OY., 1924, Mat. Sb, V31, P366

[9] ON THE FINITE GROUPS OF SUPERSOLUBLE TYPE [J].

Vasil'ev, A. F. ;

Vasil'eva, T. I. ;

Tyutyanov, V. N. .

SIBERIAN MATHEMATICAL JOURNAL, 2010, 51 (06) :1004-1012

[10] Finite groups with subnormal Schmidt subgroups [J].

Vedernikov, V. A. .

ALGEBRA AND LOGIC, 2007, 46 (06) :363-372

← 1 →