Filters in the lattice of quasivarieties of metabelian groups
Copyright policy )Filters in the lattice of quasivarieties of metabelian groups
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.
cardinalities of filters, Lattices of varieties, Solvable groups, supersolvable groups, lattices of quasivarieties, metabelian groups, Quasivarieties, Quasivarieties and varieties of groups
cardinalities of filters, Lattices of varieties, Solvable groups, supersolvable groups, lattices of quasivarieties, metabelian groups, Quasivarieties, Quasivarieties and varieties of groups
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