Schur-Zassenhaus theorem for X-permutable subgroups

被引：17

作者：

Guo, Wenbin ^{[1
,2
]}

Shum, K. P. ^{[3
]}

Skiba, Alexander N. ^{[4
]}

机构：

[1] Xuzhou Normal Univ, Dept Math, Xuzhou 221116, Jiangsu, Peoples R China

[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Peoples R China

[3] Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

[4] Gomel State Univ F Skorina, Dept Math, Gomel 246028, BELARUS

来源：

ALGEBRA COLLOQUIUM | 2008年 / 15卷 / 02期

关键词：

finite groups; X-permutable subgroups; complements; p-supersoluble groups;

D O I：

10.1142/S1005386708000187

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A and B be subgroups of a group G, and 0 not equal X subset of G. Then A is said to be X-permutable with B if there exists an element x is an element of X such that AB(x) = B(x)A. In this paper, a new version of Schur-Zassenhaus theorem is obtained for X-permutable subgroups, and hence, Question 5.1 in [6] is answered.

引用

页码：185 / 192

页数：8

共 10 条

[1]

Gorenstein D., 1980, FINITE GROUPS

[2]

GUO W, 2005, SE ASIAN B MATH, V29, P493

[3]

GUO W, 2000, THEORY CLASSES GROUP

[4]

Guo WB, 2006, PUBL MATH-DEBRECEN, V68, P433

[5] G-covering systems of subgroups for classes of p-supersoluble and p-nilpotent finite groups [J].

Guo, WB ;

Shum, KP ;

Skiba, AN .

SIBERIAN MATHEMATICAL JOURNAL, 2004, 45 (03) :433-442

[6] X-semipermutable subgroups of finite groups [J].

Guo, Wenbin ;

Shum, K. P. ;

Skiba, Alexander N. .

JOURNAL OF ALGEBRA, 2007, 315 (01) :31-41

[7]

Huppert B., 1967, GRUNDLEHREN MATH WIS, V134

[8]

Kegel O. H., 1961, ARCH MATH, V12, P90, DOI DOI 10.1007/BF01650529

[9]

ROBINSON JS, 1982, COURSE THEORY GROUPS

[10]

Weinstein M., 1982, Between Nilpotent and Solvable

← 1 →