PSL(2,Z) as a non distorted subgroup of Thompson's group T

2010/06/02 by Ariadna Fossas, Fossas, Ariadna
Mathematics · #20F65 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:20F65

paper · pdf · doi:10.48550/arxiv.1006.0508

arxiv created 2010/06/02 · openalex publication_date 2010/06/02 · arxiv updated 2010/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we characterize the elements of PSL(2,Z), as a subgroup of Thompson group T, in the language of reduced tree pair diagrams and in terms of piecewise linear maps as well. Actually, we construct the reduced tree pair diagram for every element of PSL(2,Z) in normal form. This allows us to estimate the length of the elements of PSL(2,Z) through the number of carets of their reduced tree pair diagrams and, as a consequence, to prove that PSL(2,Z) is a non distorted subgroup of T. In particular, we find non-distorted free non abelian subgroups of T.

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