Finite 2-groups with exactly one nonmetacyclic maximal subgroup.
type: Item
instance of: scholarly article
title: Finite 2-groups with exactly one nonmetacyclic maximal subgroup.
zbMATH Open document ID: 1157.20010
author: Zvonimir Janko
published in: Israel Journal of Mathematics
publication date: 2008-10-16T00:00:00Z
review text: It is well-known that a \(p\)-group which is the product of two finite cyclic groups with \(p\) an odd prime is necessarily metacyclic, and such nonmetacyclic 2-group contains exactly one nonmetacyclic maximal subgroup. The aim of the present paper is to characterize all finite 2-groups \(G\) with exactly one nonmetacyclic maximal subgroup. This turns out to be an extremely complicated task. The group \(G\) is generated by two or three elements, in the former case the group \(G\) is the product of two cyclic subgroups, in the latter case the commutator subgroup is elementary Abelian of order at most 4. In the paper all these groups are determined in terms of generators and relations and their structures are described.
reviewed by: János Kurdics
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E28
zbMATH DE Number: 5351786
zbMATH Keywords: finite 2-groups
zbMATH Keywords: products of subgroups
zbMATH Keywords: maximal subgroups
zbMATH Keywords: metacyclic groups
zbMATH Keywords: generators
zbMATH Keywords: relations
MaRDI profile type: Publication
full work available at URL: s11856-008-1033-y
OpenAlex ID: W1978035419
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DOI: 10.1007/S11856-008-1033-Y
description: scientific article; zbMATH DE number 5351786