Varieties of lattice ordered groups that contain no non-abelian o-groups are solvable

It is shown that the variety _n of lattice ordered groups defined by the identity xⁿyⁿ=yⁿxⁿ, where n is the product of k (not necessarily distinct primes) is contained in the (k+1)st power A^k+1 of the variety A of all Abelian lattice ordered groups. This implies, in particular, that _n is solvable class k + 1. It is further established that any variety V of lattice ordered groups which contains no non-Abelian totally ordered groups is necessarily contained in _n, for some positive integer n.This work was supported in part, by NSERC Grant A4044.