Finite 2-groups whose nonnormal subgroups have orders at most \(2^3\).
type: Item
instance of: scholarly article
title: Finite 2-groups whose nonnormal subgroups have orders at most \(2^3\).
zbMATH Open document ID: 1266.20028
author: Qinhai Zhang
author: Meijuan Su
published in: Frontiers of Mathematics in China
publication date: 2012-12-06T00:00:00Z
review text: \textit{D. S. Passman} [J. Algebra 15, 352-370 (1970; Zbl 0198.04404)] has classified the non-Dedekindian \(p\)-groups all of whose nonnormal subgroups have order \(p\). Later the author et al., have classified the \(p\)-groups all of whose nonnormal subgroups have orders at most \(p^2\). In this paper the \(2\)-groups all of whose nonnormal subgroups have orders at most \(2^3\), are classified. A similar problem for \(p\)-groups, \(p>2\), as the authors inform, will be published later. Note that the title groups are metabelian.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 6113020
zbMATH Keywords: finite 2-groups
zbMATH Keywords: minimal non-Abelian \(p\)-groups
zbMATH Keywords: nonnormal subgroups
zbMATH Keywords: central extensions
reviewed by: Yakov Berkovich
MaRDI profile type: Publication
full work available at URL: s11464-012-0216-3
OpenAlex ID: W2125529751
cites work: Groups of prime power order. Vol. 1.
cites work: Groups of prime power order. Vol. 2.
cites work: Groups of prime power order. Vol. 3.
cites work: Endliche Gruppen I
cites work: Nonnormal subgroups of \(p\)-groups.
cites work: FINITE GROUPS WHICH HAVE MANY NORMAL SUBGROUPS
cites work: Finite \(p\)-groups whose nonnormal subgroups have orders at most \(p^3\).
cites work: Finite p-Groups All of Whose Subgroups of Index p2 Are Abelian
DOI: 10.1007/S11464-012-0216-3
description: scientific article; zbMATH DE number 6113020