On a free group of transformations defined by an automaton

2006/01/10 by Mariya Vorobets, Vorobets, Mariya, Yaroslav Vorobets +1
Computer Science · Mathematics · #20E05 #20E08 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #msc:20E05 #msc:20E08 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0601231

19 pages, 4 figures

openalex publication_date 2006/01/10 · arxiv created 2006/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3.

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