Commensurations and Subgroups of Finite Index of Thompson's Group F

José Burillo, Sean Cleary, Claas E. Röver

Published 2007-11-06, updated 2010-03-20Version 4

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 and in terms of tree pair diagrams. We show com (F) is not finitely generated and determine which subgroups of finite index in F are isomorphic to F. We show that the natural map from the commensurator group to the quasi-isometry group of F is injective.