Fitting classes \({\mathcal F}\) such that all finite groups have \({\mathcal F}\)-injectors
type: Item
instance of: scholarly article
title: Fitting classes \({\mathcal F}\) such that all finite groups have \({\mathcal F}\)-injectors
zbMATH Open document ID: 0611.20010
DOI: 10.1007/BF02776243
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let \(\mathcal F\) be a homomorph and Fitting class such that \(E_ z\mathcal F=\mathcal F\). The authors prove that if all \(\mathcal F\)-constrained groups have \(\mathcal F\)-injectors, then all groups have \(\mathcal F\)-injectors. In particular if \(\mathcal F\) is a class of quasinilpotent groups containing the nilpotent groups, then every group has \(\mathcal F\)-injectors.
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 3987544
zbMATH Keywords: homomorph
zbMATH Keywords: Fitting class
zbMATH Keywords: \({\mathcal F}\)-constrained groups
zbMATH Keywords: \({\mathcal F}\)-injectors
zbMATH Keywords: quasinilpotent groups
author: Maria J. Iranzo
author: Francisco Pérez-Monasor
reviewed by: Rodica Covaci
MaRDI profile type: Publication
cites work: Fittingklassen endlicher Gruppen, in denen gewisse Hauptfaktoren einfach sind
cites work: Nilpotent injectors in finite groups
cites work: The \(\pi\)-layer of a finite group
cites work: Q3659962
cites work: Conjugacy classes of maximal nilpotent subgroups
cites work: Injectors and normal subgroups of finite groups
cites work: Q4073546
full work available at URL: https://doi.org/10.1007/bf02776243
OpenAlex ID: W2027097140
description: scientific article; zbMATH DE number 3987544