\({\mathcal F}\)-constraint with respect to a Fitting class
type: Item
instance of: scholarly article
title: \({\mathcal F}\)-constraint with respect to a Fitting class
zbMATH Open document ID: 0571.20012
DOI: 10.1007/BF01194184
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: Let \({\mathcal F}\) be a Fitting class and \(\pi =char {\mathcal F}=\{p|\) \(C_ p\in {\mathcal F}\}\), we say that a group G is \({\mathcal F}\)-constrained when \(C_{\bar G}(\bar G_{{\mathcal F}})\leq G_{{\mathcal F}}\), where \(\bar G=G/O_{\pi '}(G)\). We denote by \({\mathcal X}_{{\mathcal F}}\) the class of \({\mathcal F}\)-constrained groups. In this paper we prove the following results: i) \({\mathcal X}_{{\mathcal F}}\) is a Fitting class. ii) If \({\mathcal N}\subseteq {\mathcal F}\subseteq \tilde N\), then all \({\mathcal X}_{{\mathcal F}}\)-groups possess a unique conjugacy class of \({\mathcal F}\)-injectors. We analyze also the relations between two Fitting classes \({\mathcal F}\) and \({\mathcal H}\) such that \({\mathcal X}_{{\mathcal F}}={\mathcal X}_{{\mathcal H}}\).
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 3910601
zbMATH Keywords: Fitting class
zbMATH Keywords: \({\mathcal F}\)-constrained groups
zbMATH Keywords: conjugacy class of \({\mathcal F}\)-injectors
author: Maria J. Iranzo
author: Francisco Pérez-Monasor
MaRDI profile type: Publication
cites work: Fittingklassen endlicher Gruppen, in denen gewisse Hauptfaktoren einfach sind
cites work: Q4087401
cites work: The \(\pi\)-layer of a finite group
cites work: Endliche Gruppen I
cites work: Injectors and normal subgroups of finite groups
full work available at URL: https://doi.org/10.1007/bf01194184
OpenAlex ID: W2247152594
description: scientific article; zbMATH DE number 3910601