The word problem for subvarieties of the variety \({\mathfrak N}_ 2{\mathfrak A}\)
type: Item
instance of: scholarly article
title: The word problem for subvarieties of the variety \({\mathfrak N}_ 2{\mathfrak A}\)
zbMATH Open document ID: 0661.20018
DOI: 10.1007/BF01980243
author: Olga Kharlampovich
published in: Algebra and Logic
publication date: 1987-01-01T00:00:00Z
review text: The author says that a variety \({\mathfrak A}\) of universal algebras has solvable word problem if in any algebra from \({\mathfrak A}\) given in \({\mathfrak A}\) by finite numbers of generators and defining relations the word problem is solvable. Let \({\mathfrak A}\) be the variety of all abelian groups, \({\mathfrak N}_ 2\) be the variety of all 2-nilpotent groups, \({\mathfrak N}_ 2{\mathfrak A}\) be the product of varieties \({\mathfrak N}_ 2\) and \({\mathfrak A}\). These designations are also used for the corresponding varieties of Lie algebras. The main results of this work are the following: Theorem 1. In any subvariety of the variety \({\mathfrak N}_ 2{\mathfrak A}\) of groups the word problem is solvable. Theorem 2. In any subvariety of the variety \({\mathfrak N}_ 2{\mathfrak A}\) of Lie algebras over a field of characteristic \(\neq 2\) the word problem is solvable.
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 4079735
zbMATH Keywords: variety of groups
zbMATH Keywords: solvable word problem
zbMATH Keywords: generators
zbMATH Keywords: relations
zbMATH Keywords: product of varieties
zbMATH Keywords: varieties of Lie algebras
reviewed by: Leonid M. Martynov
MaRDI profile type: Publication
cites work: Q3961014
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description: scientific article; zbMATH DE number 4079735