Engel groups. I
type: Item
instance of: scholarly article
title: Engel groups. I
zbMATH Open document ID: 0708.20007
DOI: 10.1007/BF02764726
author: Arye Juhász
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: An \(n\)-Engel relator \(R\) is an \(n\)-times iterated commutator of an element \(A\) of the free group \({\mathcal F}\) by an element \(B\in{\mathcal F}\), that is to say, \(R=[A,nB]\), where \([A,0B]=A\), and \([A,nB]=[[A,(n-1)B],B]\). The paper under review is the first one of a series whose aim is a study of relatively free \(n\)-Engel groups through their presentations. It is devoted to the study of groups with a single Engel relator. Using diagrams, a description of all the consequences of this relator is given. The details are rather technical.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F06
Mathematics Subject Classification ID: 20F45
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20F12
zbMATH DE Number: 4163145
zbMATH Keywords: Engel relators
zbMATH Keywords: iterated commutators
zbMATH Keywords: free groups
zbMATH Keywords: relatively free \(n\)-Engel groups
zbMATH Keywords: presentations
zbMATH Keywords: diagrams
reviewed by: J. Huebschmann
MaRDI profile type: Publication
cites work: Spherical diagrams and identities among relations
cites work: Q5817437
cites work: Engelsche Elemente der Länge drei. (Engel elements of length three.)
cites work: Small cancellation theory with a weakened small cancellation hypothesis. I: The basic theory
cites work: Engel groups. II.
cites work: Engel groups. III.
cites work: Q5840069
cites work: Q4145882
cites work: Q5637059
cites work: Generalized small cancellation theory and applications. I. The word problem
cites work: Q5634153
full work available at URL: https://doi.org/10.1007/bf02764726
OpenAlex ID: W4243692504
description: scientific article; zbMATH DE number 4163145