A Branch Group in a Class of Non-Contracting Weakly Regular Branch Groups

2023/11/10 by Sagar Saha, Saha, Sagar, K. V. Krishna +1
Computer Science · Mathematics · #20E08 #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2311.06393

openalex publication_date 2023/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a class of non-contracting groups containing an infinite family of fractal and weakly regular branch groups, and study certain properties including abelianization, just infiniteness, and word problem. We present an example of a branch group in this class and show that it is of exponential growth. It seems this is the first example of a non-contracting branch group constructed explicitly.

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