#### 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