Non-split sharply 2- and 3-transitive groups in SL_n(\mathbb Z)
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914457875120128 |
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| author | Amelio, Marco André, Simon |
| author_facet | Amelio, Marco André, Simon |
| contents | We prove that $\mathrm{SL}_3(\mathbb{Z})$ contains a non-split sharply 2-transitive subgroup, answering a question of Glasner and Gulko. We also prove that $\mathrm{SL}_4(\mathbb{Z})$ contains a non-split sharply 3-transitive subgroup, but that $\mathrm{SL}_3(\mathbb{Z})$ does not contain an infinite sharply 3-transitive subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-split sharply 2- and 3-transitive groups in SL_n(\mathbb Z) Amelio, Marco André, Simon Group Theory Primary 20B22 We prove that $\mathrm{SL}_3(\mathbb{Z})$ contains a non-split sharply 2-transitive subgroup, answering a question of Glasner and Gulko. We also prove that $\mathrm{SL}_4(\mathbb{Z})$ contains a non-split sharply 3-transitive subgroup, but that $\mathrm{SL}_3(\mathbb{Z})$ does not contain an infinite sharply 3-transitive subgroup. |
| title | Non-split sharply 2- and 3-transitive groups in SL_n(\mathbb Z) |
| topic | Group Theory Primary 20B22 |
| url | https://arxiv.org/abs/2604.07001 |