Generalized Grigorchuk's Overgroups as points on M_k

2019/09/10 by Supun T. Samarakoon, Samarakoon, Supun T.
Computer Science · Mathematics · #20E08 #20F10 #20F65 #20F69 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1909.04575

openalex publication_date 2019/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following the construction from `Degrees of growth of finitely generated groups and the theory of invariant means' we generalize the Grigorchuk's overgroup G, studied in `On parabolic subgroups and Hecke algebras of some fractal groups' to the family \ G_ω, ω∈ Ω= \ 0, 1, 2 \^ℕ \ of generalized Grigorchuk's overgroups. We consider these groups as 8-generated and describe the closure of this family in the space M₈ of marked groups.

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