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Article overview
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A new characterization of Conrad's property for group orderings, with applications | | Adam Clay
; Andrés Navas
; Cristóbal Rivas
; | | Date: |
7 Jan 2009 | | 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. | | Source: | arXiv, 0901.0880 | | Services: | Forum | Review | PDF | Favorites | |
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