A new characterization of Conrad's property for group orderings, with applications

Abstract

We provide a pure algebraic version of the dynamical characterization of Conrad's property. This approach allows dealing with general group actions on totally ordered spaces. As an application, we give a new and somehow constructive proof of a theorem first established by Linnell: an orderable group having infinitely many orderings has uncountably many. This proof is achieved by extending to uncountable orderable groups a result about orderings which may be approximated by their conjugates. This last result is illustrated by an example of an exotic ordering on the free group given in the Appendix.

Some new comments included

References in corpus (2)

• Amenable groups that act on the line
• Isolated points in the space of left orderings of a group

Cited by in corpus (4)

• Dehornoy-like left orderings and isolated left orderings
• Nielsen-Thurston orderings and the space of braid orderings
• Locally moving groups and laminar actions on the line
• On spaces of Conradian group orderings