A new characterization of Conrad's property for group orderings, with applications
Group Theory
2014-10-01 v2 Dynamical Systems
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.
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Cite
@article{arxiv.0901.0880,
title = {A new characterization of Conrad's property for group orderings, with applications},
author = {Adam Clay and Andrés Navas and Cristóbal Rivas},
journal= {arXiv preprint arXiv:0901.0880},
year = {2014}
}
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