A characterization of the hypercyclically embedded subgroups of finite groups

被引：71

作者：

Skiba, Alexander N. ^{[1
]}

机构：

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

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2011年 / 215卷 / 03期

关键词：

MINIMAL SUBGROUPS; SYLOW SUBGROUPS; PI-QUASINORMALITY; PERMUTABLE SUBGROUPS; MAXIMAL-SUBGROUPS; C-NORMALITY;

D O I：

10.1016/j.jpaa.2010.04.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A normal subgroup H of a finite group G is said to be hypercyclically embedded in G if every chief factor of G below H is cyclic. The major aim of the present paper is to characterize the normal hypercyclically embedded subgroups E of a group G by means of the embedding of the maximal and minimal subgroups of the Sylow subgroups of the generalized Fitting subgroup of E. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：257 / 261

页数：5

共 32 条

[1]

[Anonymous], 1968, Finite Groups

[2] INFLUENCE OF PI-QUASINORMALITY ON MAXIMAL-SUBGROUPS OF SYLOW SUBGROUPS OF FITTING SUBGROUP OF A FINITE-GROUP [J].

ASAAD, M ;

RAMADAN, M ;

SHAALAN, A .

ARCHIV DER MATHEMATIK, 1991, 56 (06) :521-527

[3] The influence of minimal subgroups on the structure of finite groups [J].

Asaad, M ;

Csörgö, P .

ARCHIV DER MATHEMATIK, 1999, 72 (06) :401-404

[4] On maximal subgroups of Sylow subgroups of finite groups [J].

Asaad, M .

COMMUNICATIONS IN ALGEBRA, 1998, 26 (11) :3647-3652

[5]

Baer R., 1959, CAN J MATH, V11, P353

[6] On minimal subgroups of finite groups [J].

Ballester-Bolinches, A ;

Pedraza-Aguilera, MC .

ACTA MATHEMATICA HUNGARICA, 1996, 73 (04) :335-342

[7] Finite groups with some C-normal minimal subgroups [J].

Ballester-Bolinches, A ;

Wang, YM .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2000, 153 (02) :121-127

[8]

Ballester-Bolinches A., 2006, MATH ITS APPL, V584

[9] FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE NORMAL [J].

BUCKLEY, J .

MATHEMATISCHE ZEITSCHRIFT, 1970, 116 (01) :15-&

[10]

Doerk K., 1992, De Gruyter Exp. Math., V4, pxiv + 891

← 1 2 3 4 →