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. 
@article{AL_2021_60_2_a0,
     author = {A. I. Budkin},
     title = {Independent axiomatizability of quasivarieties of torsion-free nilpotent groups},
     journal = {Algebra i logika},
     pages = {123--136},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {2021},
     language = {ru},
     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/