A Class of Non-Contracting Branch Groups with Non-Torsion Rigid Kernels
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| author | Saha, Sagar Krishna, K. V. |
| author_facet | Saha, Sagar Krishna, K. V. |
| contents | In this work, we provide the first example of an infinite family of branch groups in the class of non-contracting self-similar groups. We show that these groups are very strongly fractal, not regular branch, and of exponential growth. Further, we prove that these groups do not have the congruence subgroup property by explicitly calculating the structure of their rigid kernels. This class of groups is also the first example of branch groups with non-torsion rigid kernels. As a consequence of these results, we also determine the Hausdorff dimension of these groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Class of Non-Contracting Branch Groups with Non-Torsion Rigid Kernels Saha, Sagar Krishna, K. V. Group Theory 20E08, 20E18 In this work, we provide the first example of an infinite family of branch groups in the class of non-contracting self-similar groups. We show that these groups are very strongly fractal, not regular branch, and of exponential growth. Further, we prove that these groups do not have the congruence subgroup property by explicitly calculating the structure of their rigid kernels. This class of groups is also the first example of branch groups with non-torsion rigid kernels. As a consequence of these results, we also determine the Hausdorff dimension of these groups. |
| title | A Class of Non-Contracting Branch Groups with Non-Torsion Rigid Kernels |
| topic | Group Theory 20E08, 20E18 |
| url | https://arxiv.org/abs/2501.04112 |