Pattern closure of groups of tree automorphisms

2010/12/08 by Zoran Šunić, Sunic, Zoran
Computer Science · Mathematics · #20E08 #22C05 #37B10 #Cellular Automata and Applications #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1012.1688

openalex publication_date 2010/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that a group defined by forbidding all patterns of size s+1 that do not appear in a given self-similar group of tree automorphisms is the topological closure of a self-similar, countable, regular branch group, branching over its level s stabilizer. As an application, it is shown that there are no infinite, finitely constrained, topologically finitely generated groups of binary tree automorphisms defined by forbidden patterns of size two.

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