ON SYLOW NORMALIZERS OF FINITE GROUPS

被引：3

作者：

Kazarin, L. S. ^{[1
]}

Martinez-Pastor, A. ^{[2
]}

Perez-Ramos, M. D. ^{[3
]}

机构：

[1] Yaroslavl P Demidov State Univ, Dept Math, Yaroslavl 150000, Russia

[2] Univ Politecn Valencia, IUMPA, Escuela Tecn Super Ingn Informat, Valencia 46022, Spain

[3] Univ Valencia, Dept Algebra, E-46100 Valencia, Spain

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2014年 / 13卷 / 03期

关键词：

Finite group; Sylow normalizer; nilpotent Hall subgroup; saturated formation; SATURATED FORMATIONS; SOLUBLE GROUPS;

D O I：

10.1142/S0219498813501168

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper considers the influence of Sylow normalizers, i.e. normalizers of Sylow subgroups, on the structure of finite groups. In the universe of finite soluble groups it is known that classes of groups with nilpotent Hall subgroups for given sets of primes are exactly the subgroup- closed saturated formations satisfying the following property: a group belongs to the class if and only if its Sylow normalizers do so. The paper analyzes the extension of this research to the universe of all finite groups.

引用

页数：20

共 22 条

[1]

[Anonymous], MATH ITS APPL

[2]

Arad Z., 1981, Houston Journal of Mathematics, V7, P23

[3] On normalizers of Sylow subgroups in finite groups [J].

Ballester-Bolinches, A ;

Shemetkov, LA .

SIBERIAN MATHEMATICAL JOURNAL, 1999, 40 (01) :1-2

[4] ON F-CRITICAL GROUPS [J].

BALLESTERBOLINCHES, A ;

PEREZRAMOS, MD .

JOURNAL OF ALGEBRA, 1995, 174 (03) :948-958

[5] Two questions of L.A. Shemetkov on critical groups [J].

BallesterBolinches, A ;

PerezRamos, MD .

JOURNAL OF ALGEBRA, 1996, 179 (03) :905-917

[6] ON FINITE-GROUPS WITH NILPOTENT SYLOW-NORMALIZERS [J].

BIANCHI, M ;

MAURI, AGB ;

HAUCK, P .

ARCHIV DER MATHEMATIK, 1986, 47 (03) :193-197

[7] BOUNDS ON THE FITTING LENGTH OF FINITE SOLUBLE GROUPS WITH SUPERSOLUBLE SYLOW NORMALIZERS [J].

BRYCE, RA ;

FEDRI, V ;

SERENA, L .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1991, 44 (01) :19-31

[8] Saturated formations closed under Sylow normalizers [J].

D'Aniello, A ;

De Vivo, C ;

Giordano, G ;

Pérez-Ramos, MD .

COMMUNICATIONS IN ALGEBRA, 2005, 33 (08) :2801-2808

[9] Saturated formations and sylow normalisers [J].

D'Aniello, A ;

De Vivo, C ;

Giordano, G .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2004, 69 (01) :25-33

[10]

D'Aniello A., 2006, P ISCH GROUP THEOR 2, P22

← 1 2 3 →