On maximal subgroups of minimax groups
type: Item
instance of: scholarly article
title: On maximal subgroups of minimax groups
zbMATH Open document ID: 0837.20045
author: F. de Giovanni
author: Silvana Franciosi
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1996-01-02T00:00:00Z
full work available at URL: https://eudml.org/doc/244086
review text: It is known, that if \(G\) is a finitely generated soluble group such that \(G/\Phi(G)\) is nilpotent then \(G\) is nilpotent too, where \(\Phi(G)\) is the Frattini subgroup of the group \(G\). J. C. Lennox proved that if \(G\) is a finitely generated soluble group such that \(G/\Phi(G)\) is finite-by- nilpotent then \(G\) is finite-by-nilpotent. The main result of this paper is Theorem. Let \(G\) be a soluble residually finite minimax group. Then \(G\) is finite-by-nilpotent if and only if it has finitely many maximal subgroups which are not normal. Corollary. Let \(G\) be a soluble residually finite minimax group such that the factor- group \(G/\Phi(G)\) is finite-by-nilpotent. Then \(G\) is finite-by- nilpotent.
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20E26
zbMATH DE Number: 817259
zbMATH Keywords: finitely generated soluble groups
zbMATH Keywords: Frattini subgroup
zbMATH Keywords: soluble residually finite minimax groups
zbMATH Keywords: finite-by-nilpotent groups
zbMATH Keywords: maximal subgroups
reviewed by: L. A. Kurdachenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 817259