l-Metabelian Varieties of Lattice-Ordered Groups
by
Michael R. Darnel
Indiana University South Bend

Medvedev proved that the abelian variety of lattice-ordered groups has only two representable covering varieties which are not weakly abelian. In the past, the author proved the existence of l-metabelian varieties covering the Medvedev varieties which are not obtained by simple lattice joins of abelian covers. This last result is improved to show that any l-metabelian cover of a Medvedev variety is one of three types: a simple lattice join of abelian covers; one of the known Darnel covers; or one having the positive infinite shifting property.

Varying the construction of a wreath product also gives an example of a countable convex subinterval of the lattice of l-metabelian varieties, in which each maximal antichain has one or two elements, and in which every totally ordered subinterval has at most two elements.

Date received: December 20, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakg-10.