This article is cited in 2 papers

Mathematical logic, algebra and number theory

Quasivarieties of nilpotent groups of axiomatic rank $4$

A. I. Budkin

Altai State University, 61, Lenina ave., Barnaul, 656049, Russia

Abstract: We say that the axiomatic rank of a quasivariety $K$ is equal to $n$ if $K$ can be defined by a system of quasi-identities in $n$ variables and cannot be defined by any set of quasi-identities in fewer variables. If there is no such $n$, then $K$ has an infinite axiomatic rank. We prove that the set of quasivarieties of nilpotent torsion-free groups of class at most $2$ of axiomatic rank $4$ is continual.

Keywords: nilpotent group, quasivariety, variety, axiomatic rank.

UDC: 512.5

MSC: 20E10

Received April 16, 2020, published December 22, 2020

Language: English

DOI: 10.33048/semi.2020.17.143

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