On the lattice of quasivarieties of nilpotent groups of class 2 (Q1288126)

Let \(G\) be a finitely generated nilpotent group of class 2 and let \(N=qG\) be the quasivariety of groups generated by \(G\). Let \(L_q(N)\) be the lattice of quasivarieties contained in \(N\). The author gives a necessary and sufficient condition for the lattice \(L_q(N)\) to be finite. Moreover, the author proves that if \(L_q(N)\) is infinite then it has the cardinality of the continuum. This fact is an extension of some theorems by \textit{A. I. Budkin} [Algebra Logika 33, No. 1, 25-36 (1994; Zbl 0823.20025)].