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 quasiidentities 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 ⊈ K ⊆ N), an interval [M, K] has the power of the continuum in the quasivariety lattice.
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Translated from Algebra i Logika, Vol. 60, No. 2, pp. 123-136,March-April, 2021. Russian https://doi.org/10.33048/alglog.2021.60.201.
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Budkin, A.I. Independent Axiomatizability of Quasivarieties of Torsion-Free Nilpotent Groups. Algebra Logic 60, 79–88 (2021). https://doi.org/10.1007/s10469-021-09630-2
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DOI: https://doi.org/10.1007/s10469-021-09630-2