Filters in the lattice of quasivarieties of metabelian groups
type: Item
instance of: scholarly article
title: Filters in the lattice of quasivarieties of metabelian groups
zbMATH Open document ID: 0905.20017
DOI: 10.1007/BF02732360
author: S. V. Lenyuk
published in: Siberian Mathematical Journal
publication date: 1998-11-22T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20E10
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 1225820
zbMATH Keywords: metabelian groups
zbMATH Keywords: lattices of quasivarieties
zbMATH Keywords: cardinalities of filters
MaRDI profile type: Publication
cites work: Q3803326
cites work: Filters in lattices of quasivarieties of algebraic systems
cites work: Q3964761
cites work: Independent axiomatizability of quasivarieties of generalized solvable groups
cites work: Quasivarieties of algebraic systems
cites work: Finiteness Conditions for Soluble Groups
cites work: On the Finiteness of Certain Soluble Groups
full work available at URL: https://doi.org/10.1007/bf02732360
OpenAlex ID: W2076903169
description: scientific article; zbMATH DE number 1225820