Amenability and Kunze-Stein property for groups acting on a tree

Claudio Nebbia

Vol. 135 (1988), No. 2, 371–380

DOI: 10.2140/pjm.1988.135.371

Abstract

We characterize the amenable groups acting on a locally finite tree. In particular if the tree is homogeneous and the group G acts transitively on the vertices then we prove that G is amenable iff G fixes one point of the boundary of the tree. Moreover we prove that a group G which acts transitively on the vertices and on an open subset of the boundary is either amenable or a Kunze-Stein group.

Mathematical Subject Classification 2000

Primary: 43A07

Secondary: 05C05, 20B27

Milestones

Received: 24 November 1986

Revised: 4 November 1987

Published: 1 December 1988