A tree-free group that is not orderable

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.

2 pages

References in corpus (2)

• Groups acting freely on $\Lambda$-trees
• Affine actions on non-archimedean trees