Commensurations and subgroups of finite index of thompson’s groupf
Röver, Claas E
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Burillo, José; Cleary, Sean; Röver, Claas E (2008). Commensurations and subgroups of finite index of thompson’s groupf. Geometry & Topology 12 , 1701-1709
We determine the abstract commensurator Com. F/ of Thompson's group F and describe it in terms of piecewise linear homeomorphisms of the real line. We show Com. F/ 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.