On periodic radical groups in which permutability is a transitive relation.
type: Item
instance of: scholarly article
title: On periodic radical groups in which permutability is a transitive relation.
zbMATH Open document ID: 1119.20044
author: Adolfo Ballester-Bolinches
author: Tatiana Pedraza
author: L. A. Kurdachenko
published in: Journal of Pure and Applied Algebra
publication date: 2007-06-26T00:00:00Z
review text: A group \(G\) is called radical, if every nontrivial quotient group of \(G\) has a nontrivial Hirsch-Plotkin radical. The authors consider periodic radical groups \(G\) with minimum condition for \(p\)-groups and transitivity for permutability. Main results: \(G\) is metabelian and its Hirsch-Plotkin radical is the direct product of the locally nilpotent residual and the upper hypercenter of \(G\) (Theorems 3 and 4).
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20F19
zbMATH DE Number: 5167571
zbMATH Keywords: periodic radical groups
zbMATH Keywords: minimum condition for \(p\)-groups
zbMATH Keywords: transitivity of permutability
zbMATH Keywords: Hirsch-Plotkin radical
zbMATH Keywords: products of subgroups
reviewed by: Hermann Heineken
MaRDI profile type: Publication
full work available at URL: j.jpaa.2006.11.006
OpenAlex ID: W1982173377
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DOI: 10.1016/J.JPAA.2006.11.006
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description: scientific article; zbMATH DE number 5167571