On Sylowizers in finite \(p\)-soluble groups.
type: Item
instance of: scholarly article
title: On Sylowizers in finite \(p\)-soluble groups.
zbMATH Open document ID: 1142.20005
author: Maria J. Iranzo
author: Julio P. Lafuente
author: Francisco Pérez-Monasor
published in: Ricerche di Matematica
publication date: 2008-06-24T00:00:00Z
review text: In a finite group \(G\) the Sylowizer of a \(p\)-subgroup \(R\) is a subgroup maximal with respect to having \(R\) a Sylow \(p\)-subgroup. This concept is due to \textit{W. Gaschütz} [Math. Z. 122, 319-320 (1971; Zbl 0234.20008)], where the question of conjugacy of the Sylowizers for \(p\)-solvable groups \(G\) was studied. \textit{A. V. Borovik} and \textit{E. I. Khukhro} [Math. Zametki 19, 401-418 (1976; Zbl 0347.20011)] found examples of Sylowizers of different orders. In this paper sufficient conditions are given for the conjugacy of the Sylowizers, such as, (1) \(p=2\) and the \(2\)-Sylow subgroups of the group \(G\) are either dihedral or quaternion; (2) the \(p\)-Sylow subgroups of the group \(G\) are of order at most \(p^3\); (3) \(p\) is an odd prime, the subgroup \(R\) is Abelian of maximal order.
reviewed by: János Kurdics
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 5292353
zbMATH Keywords: finite groups
zbMATH Keywords: \(p\)-soluble groups
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: Sylowizers
zbMATH Keywords: conjugacy
MaRDI profile type: Publication
full work available at URL: s11587-007-0012-7
OpenAlex ID: W1993377770
cites work: Q4116612
cites work: Sylowizers
cites work: Q3913574
cites work: Endliche Gruppen I
cites work: Q3659962
DOI: 10.1007/S11587-007-0012-7
description: scientific article; zbMATH DE number 5292353