#### Volume 12, issue 3 (2008)

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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