Finite groups all of whose Abelian subgroups are QTI-subgroups.
type: Item
instance of: scholarly article
title: Finite groups all of whose Abelian subgroups are QTI-subgroups.
zbMATH Open document ID: 1178.20014
author: Guohua Qian
author: Feng Tang
published in: Journal of Algebra
publication date: 2008-12-05T00:00:00Z
review text: A subgroup \(H\) of a finite group \(G\) is called a QTI-subgroup if \(C_G(x)\leq N_G(H)\) for all \(x\in H^\#\). In this note the authors classify the AQTI-groups, i.e., groups all of whose Abelian subgroups are QTI-groups. For example, if \(G\) is a non-Dedekindian \(p\)-group, then it is either \(Q_8*D_8\) (central product) of order \(2^5\), or \(|G/Z(G)|=p^2\) and \(G'\) is the unique minimal normal subgroup of \(G\).
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 5378820
zbMATH Keywords: finite groups
zbMATH Keywords: TI-subgroups
reviewed by: Yakov Berkovich
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.08.009
OpenAlex ID: W1963750275
cites work: Q3684278
cites work: Finite groups whose Abelian subgroups are TI-subgroups.
cites work: Q4200361
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cites work: Finite \(p\)-groups whose Abelian subgroups have a trivial intersection.
cites work: Trivial intersection groups
cites work: Prime graph components of finite groups
DOI: 10.1016/J.JALGEBRA.2008.08.009
description: scientific article; zbMATH DE number 5378820