On groups with many nearly maximal subgroups
type: Item
instance of: scholarly article
title: On groups with many nearly maximal subgroups
zbMATH Open document ID: 0924.20021
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1999-09-13T00:00:00Z
review text: A subgroup \(M\) of a group \(G\) is said to be nearly maximal if it has infinite index but every larger subgroup has finite index in \(G\). Now groups in which every subgroup is an intersection of maximal subgroups have been studied by several authors and are called IM-groups. Here the authors consider groups in which every subgroup of infinite index is an intersection of nearly maximal subgroups, under the name nearly IM-groups. They prove that if \(G\) is an infinite hyper-(abelian or finite) group, then \(G\) is nearly IM if and only if \(G\) is cyclic or dihedral.
reviewed by: Derek J. S. Robinson
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 1281972
zbMATH Keywords: nearly maximal subgroups
zbMATH Keywords: subgroups of infinite index
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: intersections of maximal subgroups
zbMATH Keywords: nearly IM-groups
author: Silvana Franciosi
author: F. de Giovanni
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1281972