On Covers in the Lattice of Quasivarieties of l-Groups

Abstract

In this paper, an infinite countable family of different covers of the variety of abelian lattice-ordered groups A in the lattice of quasivarieties (defined by implications of the form ∀x(w(x) = e → u(x)= e)) of l-groups Λ is constructed (Theorems 1, 2). All these covers of A have the following properties:

• 1) they do not contain non-abelian linearly ordered groups or nilpotent l-groups;

• 2) they are contained in the variety of weakly abelian latticeordered groups W;

• 3) they are metabelian.

This resarch was partially done while the author was a Visiting Professor at the Department of Mathematics and Statistics at Bowling Green State University, Bowling Green, Ohio in 1991. The author thanks the Department for its wam welcome and hospitality.