The Hausdorff dimension of the generalized Brunner-Sidki-Vieira Groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910382011973632 |
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| author | Fariña-Asategui, Jorge Garciarena, Mikel E. |
| author_facet | Fariña-Asategui, Jorge Garciarena, Mikel E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16876 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hausdorff dimension of the generalized Brunner-Sidki-Vieira Groups Fariña-Asategui, Jorge Garciarena, Mikel E. Group Theory 20E08, 28A78 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. |
| title | The Hausdorff dimension of the generalized Brunner-Sidki-Vieira Groups |
| topic | Group Theory 20E08, 28A78 |
| url | https://arxiv.org/abs/2403.16876 |