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Abstract
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.
Received: 2009-03-16
Revised: 2009-07-17
Published Online: 2009-11-20
Published in Print: 2010-May
© de Gruyter 2010
