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arXiv · 1212.1509

A tree-free group that is not orderable

Shane O. Rourke
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Abstract

I. M. Chiswell has asked whether every group that admits a free isometric action (without inversions) on a $Λ$-tree is orderable. We give an example of a multiple HNN extension $Γ$ which acts freely on a $\mathbb{Z}^2$-tree but which has non-trivial generalised torsion elements. The existence of such elements implies that $Γ$ is not orderable.

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Shane O. Rourke. 2012-12-07. A tree-free group that is not orderable. https://arxiv.org/abs/1212.1509

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