The lattice of quasivarieties of metabelian groups

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1996 English Publisher:Springer Science and Business Media LLCJournal:Algebra and Logic, volume 35, pages 310-315 (issn: 0002-5232, eissn: 1573-8302,

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Authors: Lenyuk, S. V.;

doi: 10.1007/bf02367355

The lattice of quasivarieties of metabelian groups

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Abstract

The author proves that the lattice of quasivarieties contained in the quasivariety of torsion-free groups satisfying the identity \(\forall x\forall y\;([x^2,y^2]=1)\) has the cardinality of the continuum.

Keywords

Lattices of varieties, Solvable groups, supersolvable groups, lattices of quasivarieties, metabelian groups, Quasivarieties, Quasivarieties and varieties of groups

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