Amenable, transitive and faithful actions of groups acting on trees

Pierre Fima (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Domaines: Théorie des groupes [math.GR]; Systèmes dynamiques [math.DS]

Pierre Fima. Amenable, transitive and faithful actions of groups acting on trees. 2012. ⟨hal-00675028v2⟩