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The Hausdorff dimension of the generalized Brunner-Sidki-Vieira Groups

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arxiv 2403.16876 v1 pith:GNO4OCB4 submitted 2024-03-25 math.GR

Jorge Fariña-Asategui , Mikel E. Garciarena This is my paper · ORCID
classification math.GR
keywords dimensionhausdorffadicbrunner-sidki-vieirageneralizedgroupactingautomorphisms
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abstract

We compute the Hausdorff dimension of the closure of the generalized Brunner-Sidki-Vieira group acting on the $m$-adic tree for $m\ge 2$, providing the first examples of self-similar topologically finitely generated closed subgroups of transcendental Hausdorff dimension in the group of $m$-adic automorphisms.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weakly branch actions: first-order theory, rigidity and Boston's conjecture

    math.GR 2025-07 conditional novelty 8.0 of 10

    Just-infinite branch pro-p groups introduced earlier by the author are shown to be rigid on trees obtained by deleting levels, forcing every branch action on the p-adic tree to be zero-dimensional and disproving Bosto...

  2. On a question of Ab\'ert and Vir\'ag

    math.GR 2025-05 conditional novelty 7.0 of 10

    For self-similar level-transitive groups with positive Hausdorff dimension in iterated wreath products, every nontrivial normal closed subgroup has full dimension; in general, counterexamples exist.

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