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Non-Abelian varieties of lattice-ordered groups in which every solvable $$\ell$$-group is Abelian. (Russian) Zbl 0574.06012
From the author’s introduction: ”In the present paper linearly ordered groups (l.o. groups) are constructed which possess a number of interesting properties and a variety of o-approximable $$\ell$$-groups in which solvable non-abelian $$\ell$$-groups do not exist. In particular, the l.o. group F constructed in §§ 2 and 3 possesses the following properties: F is non-abelian with the property $$e<a\ll b$$ implies $$a\ll b^{-1}ab$$; the factor group H/N of a subgroup H of F modulo a convex and normal (with respect to H) subgroup N is either abelian or non- solvable. The variety of $$\ell$$-groups $$\ell$$-var F generated by F is non-abelian and consists of o-approximable $$\ell$$-groups and each of its solvable $$\ell$$-groups is abelian. This variety is a new example of a minimal cover of the $$\ell$$-variety of the abelian $$\ell$$-groups in the lattice of varieties of $$\ell$$-groups. The description of properties of the l.o. group F or the variety $$\ell$$-var F is given in §3 or 4 resp.”
Reviewer: F.Šik

##### MSC:
 06F15 Ordered groups 08B15 Lattices of varieties 06B20 Varieties of lattices 20F60 Ordered groups (group-theoretic aspects) 20E10 Quasivarieties and varieties of groups
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