X-semipermutable subgroups of finite groups

被引：91

作者：

Guo, Wenbin ^{[1
]}

Shum, K. P.

Skiba, Alexander N.

机构：

[1] Chinese Univ Hong Kong, Fac Sci, Hong Kong, Hong Kong, Peoples R China

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

[3] Gomel State Univ, Dept Math, Gomel 246028, BELARUS

来源：

JOURNAL OF ALGEBRA | 2007年 / 315卷 / 01期

基金：

中国国家自然科学基金;

关键词：

finite group; X-semipermutable group; 2-maximal subgroup; supersoluble group; nilpotent group; hall; subgroup;

D O I：

10.1016/j.jalgebra.2007.06.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a non-empty subset of a group G. Then we call a subgroup A of G a X-semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T-1 of T there exists an element X E X such that A T-1(x) = T-1(x) A. In this paper, we study the properties of X-semipermutable subgroups. In particular, a new version of the famous Schur-Zassenhaus Theorem in terms of X-semipermutable subgroups is given. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：31 / 41

页数：11

共 11 条

[1]

[Anonymous], ENDLICHE GRUPPEN 1

[2]

[Anonymous], 1978, FINITE GROUPS

[3]

Doerk K., 1992, GRUYTER EXP MATH, V4

[4]

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

[5]

GUO W, 2003, X PERMUTABLE SUBGROU, V61

[6]

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

[7] 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

[8] G-covering subgroup systems for the classes of supersoluble and nilpotent groups [J].

Guo, WB ;

Shum, KP ;

Skiba, A .

ISRAEL JOURNAL OF MATHEMATICS, 2003, 138 (1) :125-138

[9]

HENRY G, 1982, BETWEEN NILPOTENT SO

[10]

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

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