Amenability of Bounded Automata Groups on Infinite Alphabets

2020/04/10 by Bernhard Reinke, Reinke, Bernhard
Computer Science · Mathematics · #05C81 #20E08 #22A22 #37B10 #43A07 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2004.05029

openalex publication_date 2020/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the action of groups generated by bounded activity automata with infinite alphabets on their orbital Schreier graphs. We introduce an amenability criterion for such groups based on the recurrence of the first level action. This criterion is a natural extension of the result that all groups generated by bounded activity automata with finite alphabets are amenable. Our motivation comes from the investigation of iterated monodromy groups of entire functions.

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