Characterizations of Schunck classes of finite soluble groups
type: Item
instance of: scholarly article
title: Characterizations of Schunck classes of finite soluble groups
zbMATH Open document ID: 0914.20018
published in: Journal of Algebra
publication date: 1999-06-17T00:00:00Z
review text: The motivation for this paper is the characterization of Schunck classes and saturated formations by means of certain embedding properties of their associated projectors. A subgroup \(H\) of a group \(G\) is said to be \(S\)-quasinormal in \(G\) if it permutes with every Sylow subgroup of \(G\). \(H\) is said to be \(S\)-quasinormally embedded in \(G\) if every Sylow subgroup of \(H\) is a Sylow subgroup of some \(S\)-quasinormal subgroup of \(G\). A subgroup \(H\) of a group \(G\) is said to be subnormally embedded in \(G\) if every Sylow subgroup of \(H\) is a Sylow subgroup of some subnormal subgroup of \(G\). A Schunck class \(\mathcal H\) is an \(S\)-quasinormally embedded Schunck class (respectively subnormally embedded) if for each group \(G\), every \(\mathcal H\)-projector is an \(S\)-quasinormally embedded (respectively subnormally embedded) subgroup of \(G\). The main results are two theorems obtaining that the Schunck classes \(S\)-quasinormally embedded are normally embedded Schunck classes and that the saturated formations subnormally embedded are the classes \({\mathcal H}={\mathcal S}_\pi\), for \(\pi=\text{char}({\mathcal H})\).
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D35
zbMATH DE Number: 1203894
zbMATH Keywords: quasinormal subgroups
zbMATH Keywords: Schunck classes
zbMATH Keywords: saturated formations
zbMATH Keywords: embedding properties
zbMATH Keywords: projectors
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: normally embedded Schunck classes
author: Adolfo Ballester-Bolinches
author: Mari Carmen Pedraza-Aguilera
author: M. D. Pérez-Ramos
reviewed by: Francisco Pérez-Monasor
MaRDI profile type: Publication
full work available at URL: jabr.1997.7215
OpenAlex ID: W1989016929
cites work: On quasinormal subgroups of finite groups
cites work: Finite soluble groups
cites work: Sylow-Gruppen und Subnormalteiler endlicher Gruppen
cites work: Q3744347
DOI: 10.1006/JABR.1997.7215
description: scientific article; zbMATH DE number 1203894