There are no sharply transitive subsets of $\mathrm{SL}(2,q)$ for $q\ge 13$

It was known at least to L.E. Dickson in 1901 that $S L (2, q)$ , in its natural action on $F_{q}^{2} ∖ {0}$ , 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 $S L (2, q)$ and show that they only exist when $q \in {2, 3, 5, 7, 11}$ .

There are no sharply transitive subsets of $S L (2, q)$ for $q \geq 13$

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There are no sharply transitive subsets of $S L (2, q)$ for $q \geq 13$

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There are no sharply transitive subsets of SL(2,q)SL(2,q) for q≥13q≥13

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There are no sharply transitive subsets of SL(2,q)SL(2,q) for q≥13q≥13

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There are no sharply transitive subsets of $S L (2, q)$ for $q \geq 13$

讲解博客

AI智能校验

There are no sharply transitive subsets of $S L (2, q)$ for $q \geq 13$

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AI智能校验