Finite groups with permutable complete Wielandt sets of subgroups

被引：54

作者：

Guo, Wenbin ^{[1
]}

Skiba, Alexander N. ^{[2
]}

机构：

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

[2] Francisk Skorina Gomel State Univ, Dept Math, Gomel 246019, BELARUS

来源：

JOURNAL OF GROUP THEORY | 2015年 / 18卷 / 02期

关键词：

D O I：

10.1515/jgth-2014-0045

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let W be a set of nilpotent Hall subgroups of a finite group G. We say that W is a Wielandt set if for each prime p dividing vertical bar G vertical bar there is exactly one subgroup W is an element of W such that p divides vertical bar W vertical bar. In this paper, we study the influence of Wielandt sets on the structure of G. In particular, we give conditions under which a normal subgroup of a finite group is hypercyclically embedded.

引用

页码：191 / 200

页数：10

共 22 条

[1] FINITE-GROUPS WHOSE SUBNORMAL SUBGROUPS PERMUTE WITH ALL SYLOW SUBGROUPS
AGRAWAL, RK
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 47 (01) : 77 - 83
[2] [Anonymous], 1967, Endliche Gruppen I, Die Grundlehren der Mathematischen Wissenschaften
[3] On permutable subgroups of finite groups
Asaad, M
Heliel, AA
[J]. ARCHIV DER MATHEMATIK, 2003, 80 (02) : 113 - 118
[4] Finite groups with certain subgroups of Sylow subgroups complemented
Asaad, M.
[J]. JOURNAL OF ALGEBRA, 2010, 323 (07) : 1958 - 1965
[5] Blessenohl D., 1975, MATH Z, V142, P293
[6] Doerk K., 1992, Finite Soluble Groups, V4
[7] GORENSTEIN D., 1968, FINITE GROUPS
[8] Guo W., 2000, THEORY CLASSES GROUP
[9] SE-Supplemented Subgroups of Finite Groups
Guo, Wenbin
Skiba, Alexander N.
Yang, Nanying
[J]. RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2013, 129 : 245 - 263
[10] Huppert B., 1982, Finite Groups. III

← 1 2 3 →