Groups in which every infinite subnormal subgroup is normal
type: Item
instance of: scholarly article
title: Groups in which every infinite subnormal subgroup is normal
zbMATH Open document ID: 0572.20016
DOI: 10.1016/0021-8693(85)90027-4
author: F. de Giovanni
author: Silvana Franciosi
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: In his study of T-groups (i.e. groups in which every subnormal subgroup is normal), \textit{D. J. S. Robinson} [Proc. Camb. Philos. Soc. 60, 21-38 (1964; Zbl 0123.24901)] showed that a soluble T-group is metabelian. The authors define an IT-group to be a group in which every infinite subnormal subgroup is normal and study soluble IT-groups. In particular, it is shown that if G is an infinite soluble IT-group then G'' is cyclic of prime power order so that G has derived length \(\leq 3\). More detailed results are given showing how to construct all infinite soluble IT-groups which are not T-groups.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 3912609
zbMATH Keywords: transitive normality
zbMATH Keywords: T-groups
zbMATH Keywords: subnormal subgroup
zbMATH Keywords: soluble IT-groups
zbMATH Keywords: derived length
reviewed by: M. J. Tomkinson
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90027-4
OpenAlex ID: W2011667562
cites work: Q3207177
cites work: Gruppen, in denen das Normalteilersein transitiv ist.
cites work: Q5736170
cites work: Q4177758
cites work: The vanishing of certain homology and cohomology groups
cites work: Q3961021
cites work: Homology in group theory
description: scientific article; zbMATH DE number 3912609