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Coverings in the lattice of quasivarieties of $$\ell$$-groups. (English. Russian original) Zbl 0954.06014
Sib. Math. J. 41, No. 2, 276-280 (2000); translation from Sib. Mat. Zh. 41, No. 2, 339-344 (2000).
Let $$\mathcal A$$ be the variety of abelian linearly ordered groups ($$\ell$$-groups). The authors present new examples of quasivarieties of $$\ell$$-groups that cover $$\mathcal A$$. They consider the direct wreath product of two infinite cyclic groups and define a proper linear order on it. Then they prove that the quasivarieties generated by these $$\ell$$-groups cover $$\mathcal A$$.
##### MSC:
 06F15 Ordered groups 20F60 Ordered groups (group-theoretic aspects) 08C15 Quasivarieties
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##### References:
 [1] Kargapolov M. I. andMerzlyakov Yu. I., Fundamentals of the Theory of Groups [in Russian], Nauka, Moscow (1972). [2] Isaeva O. V. andMedvedev N. Ya., ”Coverings in the lattice of quasivarieties of -groups”, Sibirsk. Mat. Zh.,33, No. 2, 102–107 (1992). · Zbl 0772.06013 [3] Kopytov V. M., Lattice-Ordered Groups [in Russian], Nauka, Moscow (1984). · Zbl 0567.06011 [4] Kurosh A. G., The Theory of Groups [in Russian], Nauka, Moscow (1967). · Zbl 0189.30801 [5] Kopytov V. M. andMedvedev N. Ya., The Theory of Lattice-Ordered Groups, Kluwer Acad. Publ., Dordrecht, Boston, and London (1994). · Zbl 0834.06015 [6] Malcev A. I., Algebraic Systems [in Russian], Nauka, Moscow (1970). · JFM 62.1103.02
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