Uniform Diameter Bounds in Branch Groups

2017/03/17 by Henry Bradford, Bradford, Henry
Mathematics · #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1703.05852

openalex publication_date 2017/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be either the Grigorchuk 2-group or one of the Gupta-Sidki p-groups. We give new upper bounds for the diameters of the quotients of G by its level stabilisers, as well as other natural sequences of finite-index normal subgroups. Our bounds are independent of the generating set, and are polylogarithmic functions of the group order, with explicit degree. Our proofs utilize a version of the profinite Solovay-Kitaev procedure, the branch structure of G, and in certain cases, results on the lower central series of G.

Citations

• On the diameter of permutation groups

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