arXiv · 2608.17371
There are no sharply transitive subsets of $\mathrm{SL}(2,q)$ for $q\ge 13$
Abstract
It was known at least to L.E. Dickson in 1901 that $\mathrm{SL}(2,q)$, in its natural action on $\mathbb{F}_q^2\setminus\{0\}$, has a sharply transitive subgroup only when $q\in\{2,3,5,7,11\}$. For $q$ prime, this result stems from Galois' letter to Chevalier in 1832. We extend this result to sharply transitive subsets of $\mathrm{SL}(2,q)$ and show that they only exist when $q\in\{2,3,5,7,11\}$.
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John Bamberg, Sam Mattheus. 2026-08-18. There are no sharply transitive subsets of $\mathrm{SL}(2,q)$ for $q\ge 13$. https://arxiv.org/abs/2608.17371
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