On generalized covering subgroups and normalizers of finite soluble groups
type: Item
instance of: scholarly article
title: On generalized covering subgroups and normalizers of finite soluble groups
zbMATH Open document ID: 0586.20009
DOI: 10.1007/BF01189976
author: Luis M. Ezquerro
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: If \(G\) is a finite soluble group, \(P\) a superpronormal subgroup of \(G\) and \(\mathfrak H\) is a Schunck class of the form \(\mathfrak H=E_{\Phi}\mathfrak F\) for some formation \(\mathfrak F\), a new conjugacy class of subgroups, namely the \((P,\mathfrak H)\)-normalizers of \(G\), is introduced, extending the results of Carter-Hawkes and Mann on normalizers. We investigate this conjugacy class of subgroups and its relations with the \((P,\mathfrak H)\)-covering subgroups introduced by Fischer and studied by \textit{U. Herzfeld} [Arch. Math. 41, 404--409 (1983; Zbl 0506.20005)].
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D35
zbMATH DE Number: 3939571
zbMATH Keywords: finite soluble group
zbMATH Keywords: superpronormal subgroup
zbMATH Keywords: Schunck class
zbMATH Keywords: formation
zbMATH Keywords: conjugacy class of subgroups
zbMATH Keywords: normalizers
zbMATH Keywords: covering subgroups
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01189976
OpenAlex ID: W2089509214
description: scientific article; zbMATH DE number 3939571