Volume 12, issue 3 (2008)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Other MSP Journals
Commensurations and subgroups of finite index of Thompson's group $F$

José Burillo, Sean Cleary and Claas E Röver

Geometry & Topology 12 (2008) 1701–1709
Abstract

We determine the abstract commensurator $Com\left(F\right)$ of Thompson’s group $F$ and describe it in terms of piecewise linear homeomorphisms of the real line. We show $Com\left(F\right)$ is not finitely generated and determine which subgroups of finite index in $F$ are isomorphic to $F$. We also show that the natural map from the commensurator group to the quasi-isometry group of $F$ is injective.

Keywords
Thompson group, commensurator
Mathematical Subject Classification 2000
Primary: 20E34, 20F65
Secondary: 26A30, 20F28