Commutators in residually finite groups.
type: Item
instance of: scholarly article
title: Commutators in residually finite groups.
zbMATH Open document ID: 1227.20034
published in: Israel Journal of Mathematics
publication date: 2011-05-05T00:00:00Z
review text: In a previous paper [Proc. Am. Math. Soc. 127, No. 9, 2583-2586 (1999; Zbl 0956.20017)] it has been shown that in a residually finite group \(G\) satisfying a law \([x,y]^n=1\) (\(n\) a prime power) the derived subgroup \(G'\) is locally finite. It seems difficult to prove the analogous result for arbitrary \(n\). However, this can be achieved under a somewhat stronger hypothesis. The paper contains a proof of the following result: Let \(n\) be a positive integer and \(G\) a residually finite group in which every product of at most 68 commutators has order dividing \(n\). Then \(G'\) is locally finite.
reviewed by: Rolf Brandl
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F12
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E10
zbMATH DE Number: 5884620
zbMATH Keywords: derived subgroup
zbMATH Keywords: exponents
zbMATH Keywords: commutator laws
zbMATH Keywords: residually finite groups
zbMATH Keywords: locally finite groups
zbMATH Keywords: locally finite derived group
zbMATH Keywords: products of commutators
author: Pavel Shumyatsky
MaRDI profile type: Publication
full work available at URL: s11856-011-0027-3
OpenAlex ID: W1989751725
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DOI: 10.1007/S11856-011-0027-3
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description: scientific article; zbMATH DE number 5884620