Growth of positive words and lower bounds of the growth rate for Thompson's groups F(p)

2005/11/18 by José Burillo, Burillo, Jose, Victor Guba +1
Computer Science · Mathematics · #05C25 #20F32 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0511474

openalex publication_date 2005/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F(p), p≥2 be the family of generalized Thompson's groups. Here F(2) is the famous Richard Thompson's group usually denoted by F. We find the growth rate of the monoid of positive words in F(p) and show that it does not exceed p+1/2. Also we describe new normal forms for elements of F(p) and, using these forms, we find a lower bound for the growth rate of F(p) in its natural generators. This lower bound asymptotically equals (p-1/2)log₂ e+1/2 for large values of p.

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