The word problem for subvarieties of the variety \({\mathfrak N}_ 2{\mathfrak A}\)
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.
scientific article; zbMATH DE number 4079735