Restricted Hausdorff spectra of q-adic automorphisms
(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.
(Less)
- author
- Fariña-Asategui, Jorge LU
- organization
- publishing date
- 2025-06
- 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
- 2025-07-28 09:45:43
@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}}, }