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2009 A new characterization of Conrad's property for group orderings, with applications
Andrés Navas, Cristóbal Rivas
Algebr. Geom. Topol. 9(4): 2079-2100 (2009). DOI: 10.2140/agt.2009.9.2079

Abstract

We provide a pure algebraic version of the first-named author’s dynamical characterization of the Conrad property for group orderings. 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 by the third author in the Appendix.

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Andrés Navas. Cristóbal Rivas. "A new characterization of Conrad's property for group orderings, with applications." Algebr. Geom. Topol. 9 (4) 2079 - 2100, 2009. https://doi.org/10.2140/agt.2009.9.2079

Information

Received: 3 March 2009; Revised: 28 August 2009; Accepted: 31 August 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1211.06009
MathSciNet: MR2551663
Digital Object Identifier: 10.2140/agt.2009.9.2079

Subjects:
Primary: 06F15, 20F60
Secondary: 57S25

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.9 • No. 4 • 2009
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