A characterization of third Engel groups
type: Item
instance of: scholarly article
title: A characterization of third Engel groups
zbMATH Open document ID: 0823.20038
DOI: 10.1007/BF01197213
author: Lucia Serena Spiezia
published in: Archiv der Mathematik
publication date: 1995-10-24T00:00:00Z
review text: The author gives a characterization of \(3\)-Engel groups by means of a combinatorial property. She defines the class \({{\mathcal E}_ 3}^*\) of those groups \(G\) satisfying the following condition: For every pair of infinite subsets \(X\), \(Y\) of \(G\), there exist \(x\) in \(X\) and \(y\) in \(Y\) such that \([x, y, y, y] = 1\) and proves that any infinite group in the class \({{\mathcal E}_ 3}^*\) is a third Engel group.
Mathematics Subject Classification ID: 20F45
Mathematics Subject Classification ID: 20E10
zbMATH DE Number: 769515
zbMATH Keywords: \(3\)-Engel groups
zbMATH Keywords: infinite subsets
zbMATH Keywords: infinite groups
MaRDI profile type: Publication
cites work: Q3829725
cites work: Engelsche Elemente der Länge drei. (Engel elements of length three.)
cites work: On three-Engel groups
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cites work: Q4100111
cites work: Varieties of groups
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cites work: Infinite locally soluble \(k\)-Engel groups
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full work available at URL: https://doi.org/10.1007/bf01197213
OpenAlex ID: W2050601220
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description: scientific article; zbMATH DE number 769515