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Restricted Hausdorff spectra of q-adic automorphisms

Fariña-Asategui, Jorge LU (2025) In Advances in Mathematics 472.
Abstract

Firstly, we completely determine the self-similar Hausdorff spectrum of the group of q-adic automorphisms where q is a prime power, answering a question of Grigorchuk. Indeed, we take a further step and completely determine its Hausdorff spectra restricted to the most important subclasses of self-similar groups, providing examples differing drastically from the previously known ones in the literature. Our proof relies on a new explicit formula for the computation of the Hausdorff dimension of closed self-similar groups and a generalization of iterated permutational wreath products. Secondly, we provide for every prime p the first examples of just infinite branch pro-p groups with zero Hausdorff dimension in Γp, giving strong... (More)

Firstly, we completely determine the self-similar Hausdorff spectrum of the group of q-adic automorphisms where q is a prime power, answering a question of Grigorchuk. Indeed, we take a further step and completely determine its Hausdorff spectra restricted to the most important subclasses of self-similar groups, providing examples differing drastically from the previously known ones in the literature. Our proof relies on a new explicit formula for the computation of the Hausdorff dimension of closed self-similar groups and a generalization of iterated permutational wreath products. Secondly, we provide for every prime p the first examples of just infinite branch pro-p groups with zero Hausdorff dimension in Γp, giving strong evidence against a well-known conjecture of Boston.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Branch groups, Hausdorff dimension, q-adic automorphisms, Restricted Hausdorff spectra, Self-similar groups
in
Advances in Mathematics
volume
472
article number
110294
publisher
Academic Press
external identifiers
  • scopus:105003175690
ISSN
0001-8708
DOI
10.1016/j.aim.2025.110294
language
English
LU publication?
yes
id
e867294d-0e37-4e64-9acb-aa91ee22d023
date added to LUP
2025-07-28 09:45:06
date last changed
2025-10-14 09:49:58
@article{e867294d-0e37-4e64-9acb-aa91ee22d023,
  abstract     = {{<p>Firstly, we completely determine the self-similar Hausdorff spectrum of the group of q-adic automorphisms where q is a prime power, answering a question of Grigorchuk. Indeed, we take a further step and completely determine its Hausdorff spectra restricted to the most important subclasses of self-similar groups, providing examples differing drastically from the previously known ones in the literature. Our proof relies on a new explicit formula for the computation of the Hausdorff dimension of closed self-similar groups and a generalization of iterated permutational wreath products. Secondly, we provide for every prime p the first examples of just infinite branch pro-p groups with zero Hausdorff dimension in Γ<sub>p</sub>, giving strong evidence against a well-known conjecture of Boston.</p>}},
  author       = {{Fariña-Asategui, Jorge}},
  issn         = {{0001-8708}},
  keywords     = {{Branch groups; Hausdorff dimension; q-adic automorphisms; Restricted Hausdorff spectra; Self-similar groups}},
  language     = {{eng}},
  publisher    = {{Academic Press}},
  series       = {{Advances in Mathematics}},
  title        = {{Restricted Hausdorff spectra of q-adic automorphisms}},
  url          = {{http://dx.doi.org/10.1016/j.aim.2025.110294}},
  doi          = {{10.1016/j.aim.2025.110294}},
  volume       = {{472}},
  year         = {{2025}},
}