Filters in the lattice of quasivarieties of metabelian groups (Q1271990)

The author gives a negative answer to a question posed by \textit{A. I. Budkin}: Is every nontrivial filter in the lattice of quasivarieties of torsion-free metabelian groups countable [The Kourovka notebook. Unsolved problems in group theory, 13th ed., Institute of Mathematics, Novosibirsk (1995; Zbl 0838.20001)]. The author proves that each nontrivial filter in the lattice of quasivarieties of torsion-free metabelian groups has the power of the continuum.