Groups whose non-normal subgroups have a transitive normality relation
type: Item
instance of: scholarly article
title: Groups whose non-normal subgroups have a transitive normality relation
zbMATH Open document ID: 1013.20029
DOI: 10.1007/BF02844426
author: Alessio Russo
author: Giovanni Vincenzi
publication date: 2003-03-18T00:00:00Z
review text: The structure of T-groups (or groups for which the normality relation in \(G\) is transitive), were described by Gaschütz for finite soluble groups and by Robinson for infinite soluble groups. Later, Romalis and Sesekin investigated the meta-Hamiltonian groups or groups whose non-normal subgroups are Abelian. The class of minimal-non-T groups and the \(\mathcal X\)-groups or groups in which every non-normal subgroup is a T-group are investigated. In this paper, the soluble \(\mathcal X\)-groups are studied. It is proved that they can be periodic or meta-Hamiltonian. Also, it is obtained that the periodic soluble \(\mathcal X\)-groups have derived length at most 4.
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 1884330
zbMATH Keywords: transitive normality
zbMATH Keywords: meta-Hamiltonian groups
zbMATH Keywords: T-groups
zbMATH Keywords: soluble groups
zbMATH Keywords: periodic groups
reviewed by: Francisco Pérez-Monasor
MaRDI profile type: Publication
cites work: Groups with restricted non-normal subgroups
cites work: Infinite nonabelian groups in which all infinite nonabelian subgroups are invariant
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published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 1884330