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

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

2007-11-06

arxiv.org/abs/0711.0919v4

Geometry & Topology 12 (2008) 1701-1709

Mathematics

Group Theory

9 pages

Scientific paper

10.2140/gt.2008.12.1701

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.

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