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Algebra Logika, 2019, Volume 58, Number 3, Pages 320–333 (Mi al897)  

$\omega$-Independent bases for quasivarieites of torsion-free groups

A. I. Budkin

Altai State University, Barnaul

Abstract: It is proved that there exists a set $\mathcal{R}$ of quasivarieties of torsion-free groups which (a) have an $\omega$-independent basis of quasi-identities in the class $\mathcal{K}_{0}$ of torsion-free groups, (b) do not have an independent basis of quasi-identities in $\mathcal{K}_{0}$, and (c) the intersection of all quasivarieties in $\mathcal{R}$ has an independent quasi-identity basis in $\mathcal{K}_{0}$. The collection of such sets $\mathcal{R}$ has the cardinality of the continuum.

Keywords: quasivariety, quasi-identity, independent basis, $\omega$-independent basis, torsion-free group.

DOI: https://doi.org/10.33048/alglog.2019.58.302

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UDC: 512.57
Received: 19.04.2018
Revised: 24.09.2019

Citation: A. I. Budkin, “$\omega$-Independent bases for quasivarieites of torsion-free groups”, Algebra Logika, 58:3 (2019), 320–333

Citation in format AMSBIB
\Bibitem{Bud19}
\by A.~I.~Budkin
\paper $\omega$-Independent bases for quasivarieites
of torsion-free groups
\jour Algebra Logika
\yr 2019
\vol 58
\issue 3
\pages 320--333
\mathnet{http://mi.mathnet.ru/al897}
\crossref{https://doi.org/10.33048/alglog.2019.58.302}


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