This article is cited in 3 papers

Mathematical logic, algebra and number theory

On the $\omega $-independence of quasivarieties of nilpotence groups

A. I. Budkin

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

Abstract: We prove that there exists a set $\mathcal{R}$ of quasivarieties of nilpotent groups of class two any quasivariety from $\mathcal{R} $ does not have an independent basis of quasi-identities to the class $\mathcal{N}_{2}$ of $2$-nilpotent groups and has an $\omega $-independent basis of quasi-identities to $\mathcal{N}_{2}$. The intersection of all quasivarieties in $\mathcal{R}$ has an independent basis of quasi-identities to $\mathcal{N}_{2}$. The set of such sets $\mathcal{R}$ is continual.

Keywords: nilpotent group, quasivariety, $\omega $-independence.

UDC: 512.5

MSC: 20E10

Received April 8, 2018, published April 16, 2019

DOI: 10.33048/semi.2019.16.033

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