On \(\pi\)-normally embedded subgroups of finite soluble groups
type: Item
instance of: scholarly article
title: On \(\pi\)-normally embedded subgroups of finite soluble groups
zbMATH Open document ID: 0952.20015
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1997-08-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108402
review text: The authors consider the following condition where \(\pi\) is a set of primes: A subgroup \(H\) of a group \(G\) is said to be \(\pi\)-normally embedded if a Hall \(\pi\)-subgroup of \(H\) is a Hall \(\pi\) subgroup of some normal subgroup of \(G\). This generalizes the concept of \(p\)-normally embedded subgroups which is the case when \(\pi=\{p\}\). In this very nice paper a number of results for \(p\)-normally embedded subgroups are generalized as appropriate to the situation for \(\pi\)-normally embedded subgroups. As an example here is Theorem 1. Let \(\mathcal F\) be a saturated formation. If \(G\) is a group with Abelian Hall \(\pi\)-subgroups, then \(\mathcal F\)-normalizers of \(G\) are \(\pi\)-normally embedded.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 1021764
zbMATH Keywords: \(\pi\)-normally embedded subgroups
zbMATH Keywords: finite soluble groups
zbMATH Keywords: \(p\)-normally embedded subgroups
zbMATH Keywords: saturated formations
zbMATH Keywords: Hall \(\pi\)-subgroups
zbMATH Keywords: \(\mathcal F\)-normalizers
author: Adolfo Ballester-Bolinches
author: Mari Carmen Pedraza-Aguilera
author: M. D. Pérez-Ramos
reviewed by: A. R. Camina
MaRDI profile type: Publication
cites work: Permutability in finite soluble groups
cites work: \(\Pi\)-normally embedded subgroups of finite soluble groups
cites work: p-normally embedded subgroups of finite soluble groups
cites work: Finite soluble groups
cites work: On pronormal subgroups of finite soluble groups
cites work: Q3941589
description: scientific article; zbMATH DE number 1021764