Locally compact groups acting on trees

Roger C. Alperin

Vol. 100 (1982), No. 1, 23–32

DOI: 10.2140/pjm.1982.100.23

Abstract

Following Serre’s original description of groups having the fixed point property for actions on trees, Bass has introduced the notion of a group of type FA′. Groups of type FA′ can not be nontrivial free products with amalgamation. We show that a locally compact (hausdorff) topological group with a compact set of connected components is of type FA′. Furthermore, any locally compact group which is a nontrivial free product with amalgamation has an open amalgamated subgroup.

Mathematical Subject Classification 2000

Primary: 22D05

Secondary: 20E06

Milestones

Received: 14 May 1980

Revised: 30 September 1980

Published: 1 May 1982