Amenable, transitive and faithful actions of groups acting on trees
Group Theory
2012-09-21 v2 Dynamical Systems
Abstract
We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.
Keywords
Cite
@article{arxiv.1202.6467,
title = {Amenable, transitive and faithful actions of groups acting on trees},
author = {Pierre Fima},
journal= {arXiv preprint arXiv:1202.6467},
year = {2012}
}
Comments
v.2: minor changes, final version, to appear in Annales de l'Institut Fourier