×

zbMATH — the first resource for mathematics

Engel lattice-ordered groups. (English. Russian original) Zbl 0852.06007
Algebra Logic 34, No. 4, 219-222 (1995); translation from Algebra Logika 34, No. 4, 398-404 (1995).
The author proves that any Engel lattice-ordered group (\(l\)-group) which generates a proper normal-valued variety of \(l\)-groups is \(o\)-approximable and that the Engel \(l\)-groups from any proper normal-valued variety of \(l\)-groups form a torsion class.
MSC:
06F15 Ordered groups
20F60 Ordered groups (group-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] W. C. Holland, ?The largest proper variety of lattice ordered groups,?Proc. Am. Math. Soc.,57, 25-28 (1976). · Zbl 0339.06011
[2] V. M. Kopytov and N. Ya. Medvedev, ?Varieties of lattice-ordered groups,?Usp. Mat. Nauk,4, No. 3, 117-128 (1985).
[3] V. M. Kopytov and N. Ya. Medvedev, ?Open questions in the theory of partially groups,? inProc. 5th Siberian School on Varieties of Algebraic Systems, Barnaul (1988).
[4] D. M. Smirnov, ?Infrainvariant subgroups,?Uch. Zap. Ivanov. Ped. Inst.,4, 92-96 (1953).
[5] V. M. Kopytov, ?Lattice-ordered, locally nilpotent groups,?Algebra Logika,14, No. 4, 407-413 (1975).
[6] N. Ya. Medvedev, ?o-Approximability of bounded Engell-groups,?Algebra Logika,27, No. 4, 418-421 (1988).
[7] S. A. Gurchenkov and V. M. Kopytov, ?Description of covers of the variety of Abelian lattice-ordered groups,?Sib. Mat. Zh.,28, No. 3, 66-69 (1987). · Zbl 0622.06014
[8] S. A. Gurchenkov, ?Covers in the lattice ofl-varieties,?Mat. Zametki,35, No. 5, 677-683 (1984).
[9] C. Holland, ?Varieties ofl-groups are torsion classes,?Czech. Math. J.,29, 130-131 (1985). · Zbl 0564.06008
[10] M. Darnel, ?Disjoint conjugate chains,? inOrdered Algebraic Structures (The 1991 Conrad Conference), J. Martinez and C. Holland (eds.), Kluwer (1993), pp. 31-49. · Zbl 0792.06014
[11] N. Ya. Medvedev, ?Certain issues in the theory of partially ordered groups,?Algebra Logika,22, No. 4, 435-442 (1983).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.