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On spaces of Conradian group orderings. (English) Zbl 1192.06015

Summary: We classify \(C\)-orderable groups admitting only finitely many \(C\)-orderings. We show that if a \(C\)-orderable group has infinitely many \(C\)-orderings, then it has uncountably many \(C\)-orderings, and none of these is isolated in the space of \(C\)-orderings. We carefully study the case of the Baumslag-Solitar group \(B(1, 2)\) and show that it has four \(C\)-orderings, each of which is bi-invariant, but that its space of left-orderings is homeomorphic to the Cantor set.

MSC:

06F15 Ordered groups
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