A tree-free group that is not orderable

2012/12/07 by Shane O. Rourke, Rourke, Shane O.
Mathematics · #20E08 #20F60 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E08 #msc:20F60

paper · pdf · doi:10.48550/arxiv.1212.1509

2 pages

arxiv created 2012/12/07 · arxiv updated 2012/12/10

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 ℤ²-tree but which has non-trivial generalised torsion elements. The existence of such elements implies that Γ is not orderable.

Related

• Examples of left-orderable and non-left-orderable HNN extensions
• Groups acting freely on Λ-trees
• Non-bi-orderable one-relator groups without generalized torsion
• Quasi-actions whose quasi-orbits are quasi-isometric to trees
• A finitely presented torsion-free simple group