The Higman--Thompson groups $V_n$ are $(2,2,2)$-generated
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909388980092928 |
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| author | Schesler, Eduard Skipper, Rachel Wu, Xiaolei |
| author_facet | Schesler, Eduard Skipper, Rachel Wu, Xiaolei |
| contents | We provide a family of generating sets $S_α$ of the Higman--Thompson groups $V_n$ that are parametrized by certain sequences $α$ of elements in $V_n$. These generating sets consist of $3$ involutions $σ$, $τ$, and $s_α$, where the latter involution is inspired by the class of spinal elements in the theory of branch groups. In particular this shows the existence of generating sets of $V_n$ that consist of $3$ involutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Higman--Thompson groups $V_n$ are $(2,2,2)$-generated Schesler, Eduard Skipper, Rachel Wu, Xiaolei Group Theory 20F05, 20E32 We provide a family of generating sets $S_α$ of the Higman--Thompson groups $V_n$ that are parametrized by certain sequences $α$ of elements in $V_n$. These generating sets consist of $3$ involutions $σ$, $τ$, and $s_α$, where the latter involution is inspired by the class of spinal elements in the theory of branch groups. In particular this shows the existence of generating sets of $V_n$ that consist of $3$ involutions. |
| title | The Higman--Thompson groups $V_n$ are $(2,2,2)$-generated |
| topic | Group Theory 20F05, 20E32 |
| url | https://arxiv.org/abs/2411.09069 |