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arXiv · 2604.07001

Non-split sharply 2- and 3-transitive groups in SL_n(\mathbb Z)

Marco Amelio·Simon André
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Abstract

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.

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Marco Amelio, Simon André. 2026-04-08. Non-split sharply 2- and 3-transitive groups in SL_n(\mathbb Z). https://arxiv.org/abs/2604.07001

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