Volume 17, issue 2 (2013)

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Addendum to “Commensurations and subgroups of finite index of Thompson's group $F$”

José Burillo, Sean Cleary and Claas E Röver

Geometry & Topology 17 (2013) 1199–1203
Abstract

We show that the abstract commensurator of F is composed of four building blocks: two isomorphism types of simple groups, the multiplicative group of the positive rationals and a cyclic group of order two. The main result establishes the simplicity of a certain group of piecewise linear homeomorphisms of the real line.

Keywords
Thompson's group, commensurations, simple group
Mathematical Subject Classification 2010
Primary: 20E32, 20E34
Secondary: 20F65, 20E36
References
Publication
Received: 24 September 2012
Revised: 20 December 2012
Accepted: 30 January 2013
Published: 29 May 2013
Proposed: Walter Neumann
Seconded: Benson Farb, Ronald Stern
Authors
José Burillo
Departament de Matemàtica Aplicada IV
Universitat Politècnica de Catalunya
Escola Politècnica Superior de Castelldefels
Esteve Terrades, 5
08860 Castelldefels
Spain
http://www-ma4.upc.edu/~burillo/
Sean Cleary
Department of Mathematics R8133
The City College of New York
160 Convent Ave
New York, NY 10031
USA
http://www.sci.ccny.cuny.edu/~cleary
Claas E Röver
School of Mathematics, Statistics and Applied Mathematics
National University of Ireland
University Road
Galway
Ireland
http://www.maths.nuigalway.ie/~chew/