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ON SYLOW NORMALIZERS OF FINITE GROUPS

Department of Mathematics, Yaroslavl P. Demidov State University, Sovetskaya Str 14, 150000 Yaroslavl, Russia

Escuela Técnica Superior de Ingeniería Informática, Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022 Valencia, Spain

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M. D. PÉREZ-RAMOS

Departament d'Àlgebra, Universitat de València, C/ Doctor Moliner 50, 46100 Burjassot, València, Spain

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https://doi.org/10.1142/S0219498813501168Cited by:3 (Source: Crossref)

Abstract

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.

Dedicated to the memory of Leonid A. Shemetkov (1937–2013)

Keywords:

AMSC: 20D20, 20F17

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