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A
new characterization of Conrad's property for group
orderings, with applications
Andrés Navas and Cristóbal RivasAppendix: Adam Clay |
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Algebraic & Geometric Topology 9 (2009) 2079–2100
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Abstract |
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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. |
Keywords
group orders, Conrad's property
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Mathematical Subject Classification 2000
Primary: 06F15, 20F60
Secondary: 57S25
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References |
Publication
Received: 3 March 2009
Revised: 28 August 2009
Accepted: 31 August 2009
Published: 16 October 2009
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Authors |
| Andrés Navas | |
| Departamento de Matemática y Ciencia
de la Computación Facultad de Ciencia Universidad de Santiago de Chile Alameda 3363 Estación Central Santiago Chile |
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| Cristóbal Rivas | |
| Departamento de Matemáticas Facultad de Ciencia Universidad de Chile Las Palmeras 3425 Ñuñoa Santiago Chile |
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| Adam Clay | |
| Department of Mathematics University of British Columbia Vancouver British Columbia Canada V6T 1Z2 |
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| http://www.math.ubc.ca/~aclay/ | |
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