This article is cited in 3 papers

On the quasivarieties generated by a finite group and lacking any independent bases of quasi-identities

A. I. Budkin

Altai State University, Barnaul

Abstract: Let ${\Cal R}_{p^k}$ be the variety of $2$-nilpotent groups of exponent $p^k$ with commutator subgroup of exponent $p$ ($p$ is a prime). We prove the infinity of the set of the subquasivarieties of ${\Cal R}_{p^k}$ $(k\geq 2)$ generated by a finite group and lacking any independent bases of quasi-identities.

Keywords: quasivariety, quasi-identity, independent basis, nilpotent group.

UDC: 512.54

MSC: 35R30

Received: 24.01.2020
Revised: 05.05.2020
Accepted: 17.06.2020

DOI: 10.33048/smzh.2020.61.603

 English version: Siberian Mathematical Journal, 2020, 61:6, 983–993

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