Abstract
It is shown that the variety ℒ n of lattice ordered groups defined by the identity x n y n =y n x n, 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 ℒ 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 ℒ n , for some positive integer n.
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Communicated by A. M. W. Glass
This work was supported in part, by NSERC Grant A4044.
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Reilly, N.R. Varieties of lattice ordered groups that contain no non-abelian o-groups are solvable. Order 3, 287–297 (1986). https://doi.org/10.1007/BF00400292
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DOI: https://doi.org/10.1007/BF00400292