Varieties of \(\ell\)-groups with the identity \([x^ p,y^ p]=e\) have finite bases
type: Item
instance of: scholarly article
title: Varieties of \(\ell\)-groups with the identity \([x^ p,y^ p]=e\) have finite bases
zbMATH Open document ID: 0544.06013
DOI: 10.1007/BF01979697
author: S. A. Gurchenkov
published in: Algebra and Logic
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/187254
review text: Let p be a prime. Let us denote by \({\mathcal L}_ p\) the variety of lattice ordered groups defined by the identity \([x^ p,y^ p]=e\). This paper contains the following two main results: 1) All proper subvarieties of the variety \({\mathcal L}_ p\) are constructively described. 2) It is proved that each subvariety of \({\mathcal L}_ p\) possesses a finite basis of identities.
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 20F60
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 3865354
zbMATH Keywords: variety of lattice ordered groups
zbMATH Keywords: finite basis of identities
reviewed by: Ján Jakubík
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3865354