Abstract
We prove that every variety of m-groups is a torsion class; find basis of identities for a product variety of m-groups; and show that the product of every finitely based variety of m-groups and a variety of Abelian m-groups is a finitely based variety.
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REFERENCES
M. Giraudet and J. Rachunek, “Varieties of half lattice-ordered groups of monotonic permutations of chains, ” Czech. Math. J., 49, No. 4, 743–766 (1999).
V. M. Kopytov, Lattice-Ordered Groups [in Russian], Nauka, Moscow (1984).
V. M. Kopytov and N. Ya. Medvedev, The Theory of Lattice-Ordered Groups, Kluwer, Dordrecht (1994).
M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], 2nd edn., Nauka, Moscow (1977).
V. M. Kopytov and J. Rachunek, “The greatest proper variety of m-groups, ” Algebra Logika, 42, No. 5, 624–635 (2003).
M. E. Huss and N. R. Reilly, “On reversing the order of lattice ordered groups, ” J. Alg., 91, No. 1, 176–191 (1984).
W. Ch. Holland, “Varieties of _-groups are torsion classes, ” Czech. Math. J., 29, No. 1, 11–12 (1979).
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Isaeva, O.V. Varieties and Torsion Classes of m-Groups. Algebra and Logic 42, 382–386 (2003). https://doi.org/10.1023/B:ALLO.0000004171.34849.1b
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DOI: https://doi.org/10.1023/B:ALLO.0000004171.34849.1b