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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 \(\mathcal A\).
06F15 Ordered groups
20F60 Ordered groups (group-theoretic aspects)
08C15 Quasivarieties
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