Addendum to ``Commensurations and Subgroups of
Finite Index of Thompson's Group $F$''
José Burillo, Sean Cleary, Claas Röver
Keywords
simple group,Thompson's group,commensurator
Abstract
It is shown 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.
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