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Partial orders on Dlab groups. (English. Russian original) Zbl 0974.06012
Algebra Logika 40, No. 2, 135-157 (2001); translation in Algebra Logic 40, No. 2, 75-86 (2001).
For every subgroup \(H\) of rank \(1\) in a multiplicative group of positive reals, complete descriptions are presented for maximal partial orders and for minimal isolated partial orders on the following Dlab groups: \(D_{H}({\mathbb I})\), \(D_{H*}({\mathbb I})\), \(D_{*H}({\mathbb I})\), and \({\overline{D}}_{H}({\mathbb I})\) of the unit interval \({\mathbb I}=[0,1]\) and \(D_{H}\) and \(D_{H*}\) of the extended real line \(\mathbb{\overline{R}}\). It is worth noting that W. Ch. Holland [in: Algebra, Proc. Int. Conf. Memory A. I. Mal’tsev, Novosibirsk/USSR 1989, Contemp. Math. 131, Pt. 1, 197-207 (1992; Zbl 0766.06015)] gave a description for minimal and maximal partial orders of the group \(A(\mathbb R)\) of all order automorphisms of the linearly ordered set \(\mathbb R\) of reals.

06F15 Ordered groups
20F60 Ordered groups (group-theoretic aspects)
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