Geodesic
Independent axiomatizability of quasivarieties of torsion-free nilpotent groups
Algebra i logika, Tome 60 (2021) no. 2, pp. 123-136.

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Let $N$ be a quasivariety of torsion-free nilpotent groups of class at most two. It is proved that the set of subquasivarieties in $N$, which have no independent basis of quasi-identities and are generated by a finitely generated group, is infinite. It is stated that there exists an infinite set of quasivarieties $M$ in $N$ which are generated by a finitely generated group and are such that for every quasivariety $K$ ($M\varsubsetneq K\subseteq N$), an interval $[M,K]$ has the power of the continuum in the quasivariety lattice.
Keywords: nilpotent group, quasivariety, variety, independent basis of quasi-identities. 
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     title = {Independent axiomatizability of quasivarieties of torsion-free nilpotent groups},
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     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_2_a0/}
}
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A. I. Budkin. Independent axiomatizability of quasivarieties of torsion-free nilpotent groups. Algebra i logika, Tome 60 (2021) no. 2, pp. 123-136. http://geodesic.mathdoc.fr/item/AL_2021_60_2_a0/

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