Filters in the lattice of quasivarieties of metabelian groups (Q1271990)
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scientific article; zbMATH DE number 1225820
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Filters in the lattice of quasivarieties of metabelian groups |
scientific article; zbMATH DE number 1225820 |
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Filters in the lattice of quasivarieties of metabelian groups (English)
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22 November 1998
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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.
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metabelian groups
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lattices of quasivarieties
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cardinalities of filters
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