Vol. 100, No. 1, 1982

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ISSN: 0030-8730
Locally compact groups acting on trees

Roger C. Alperin

Vol. 100 (1982), No. 1, 23–32
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 FAcan 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
Authors
Roger C. Alperin
San Jose State University