On self-similarity of finitely generated torsion-free nilpotent groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908549814157312 |
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| author | Berlatto, Adilson Santos, Tulio |
| author_facet | Berlatto, Adilson Santos, Tulio |
| contents | This paper aims to investigate the self-similarity property in finitely-generated torsion-free nilpotent groups. We establish connections between geometric equivalence and self-similarity in these groups. Moreover, we show that any 2-generated torsion-free nilpotent group of class 3 has a faithful representation as a transitive self-similar group. Additionally, we provide an example of a 4-generated torsion-free nilpotent group of class 3 that does not admit such a representation. This example, sourced from the work of V. Bludov and B. Gusev in \cite{BG}, resolves a question posed by S. Sidki in \cite{LectureDusseldorf}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On self-similarity of finitely generated torsion-free nilpotent groups Berlatto, Adilson Santos, Tulio Group Theory This paper aims to investigate the self-similarity property in finitely-generated torsion-free nilpotent groups. We establish connections between geometric equivalence and self-similarity in these groups. Moreover, we show that any 2-generated torsion-free nilpotent group of class 3 has a faithful representation as a transitive self-similar group. Additionally, we provide an example of a 4-generated torsion-free nilpotent group of class 3 that does not admit such a representation. This example, sourced from the work of V. Bludov and B. Gusev in \cite{BG}, resolves a question posed by S. Sidki in \cite{LectureDusseldorf}. |
| title | On self-similarity of finitely generated torsion-free nilpotent groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2509.16947 |