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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 516–522 (Mi semr1075)  

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.

DOI: https://doi.org/10.33048/semi.2019.16.033

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Bibliographic databases:

UDC: 512.5
MSC: 20E10
Received April 8, 2018, published April 16, 2019

Citation: A. I. Budkin, “On the $\omega $-independence of quasivarieties of nilpotence groups”, Sib. Èlektron. Mat. Izv., 16 (2019), 516–522

Citation in format AMSBIB
\Bibitem{Bud19}
\by A.~I.~Budkin
\paper On the $\omega $-independence of quasivarieties of nilpotence groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 516--522
\mathnet{http://mi.mathnet.ru/semr1075}
\crossref{https://doi.org/10.33048/semi.2019.16.033}


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