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A tree-free group that is not orderable


Author: Shane O Rourke
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
Published electronically: August 22, 2014
MathSciNet review: 3272730
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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.


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Additional Information

Shane O Rourke
Affiliation: Department of Mathematics, Cork Institute of Technology, Rossa Avenue, Cork, Ireland
Email: shane.orourke@cit.ie

DOI: https://doi.org/10.1090/S0002-9939-2014-12191-5
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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