A tree-free group that is not orderable
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- by Shane O Rourke
- Proc. Amer. Math. Soc. 143 (2015), 41-43
- DOI: https://doi.org/10.1090/S0002-9939-2014-12191-5
- Published electronically: August 22, 2014
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Abstract:
I. M. Chiswell has asked whether every group that admits a free isometric action (without inversions) on a $\Lambda$-tree is orderable. We give an example of a multiple HNN extension $\Gamma$ which acts freely on a $\mathbb {Z}^2$-tree but which has non-trivial generalised torsion elements. The existence of such elements implies that $\Gamma$ is not orderable.References
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Bibliographic Information
- Shane O Rourke
- Affiliation: Department of Mathematics, Cork Institute of Technology, Rossa Avenue, Cork, Ireland
- Email: shane.orourke@cit.ie
- Received by editor(s): November 29, 2012
- Received by editor(s) in revised form: March 1, 2013
- Published electronically: August 22, 2014
- Additional Notes: The author would like to thank Ian Chiswell for helpful conversations.
- Communicated by: Kevin Whyte
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 41-43
- MSC (2010): Primary 20E08; Secondary 20F60
- DOI: https://doi.org/10.1090/S0002-9939-2014-12191-5
- MathSciNet review: 3272730