The Abelianization of hypercyclic groups.
type: Item
instance of: scholarly article
title: The Abelianization of hypercyclic groups.
zbMATH Open document ID: 1147.20029
published in: Central European Journal of Mathematics
publication date: 2008-06-25T00:00:00Z
review text: It was shown in the literature that the Abelianization of a hypercentral group has a considerable influence on the structure of the group itself. Since hypercentral groups are hypercyclic groups, it is natural to ask whether the results obtained for hypercentral groups extend to hypercyclic groups. In the article under review, different aspects of this question are studied and the more substantial results obtained for a hypercyclic group \(G\) are the following: a) If \(G/G'\) is \(2\)-divisible, then \(G\) is \(2\)-divisible; b) if \(G/G'\) is \(2'\)-divisible, then \(G\) is \(2'\)-divisible; if \(G/G'\) is divisible-by-finite of odd order, then \(G/V\) is divisible-by-finite of odd order, where \(V\) is the intersection of the lower central series of \(O_{2'}(G)\).
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 5292954
zbMATH Keywords: hypercyclic groups
zbMATH Keywords: hypercentral groups
zbMATH Keywords: divisible-by-finite groups
zbMATH Keywords: lower central series
author: B. A. F. Wehrfritz
reviewed by: Bùi Xuân Hải
MaRDI profile type: Publication
full work available at URL: s11533-007-0030-4
OpenAlex ID: W2017927169
cites work: On Hypercentral GroupsGWith |G:Gn|<∞
cites work: Q5654235
cites work: Q5676405
cites work: On hypercentral groups.
DOI: 10.2478/S11533-007-0030-4
description: scientific article; zbMATH DE number 5292954