The non-existence of sharply $2$-transitive sets of permutations in $\mathrm{Sp}(2d,2)$ of degree $2^{2d-1} \pm 2^{d-1}$

Dominik Barth

doi:10.1007/s13366-016-0298-2

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arXiv · 1602.05164

The non-existence of sharply $2$-transitive sets of permutations in $\mathrm{Sp}(2d,2)$ of degree $2^{2d-1} \pm 2^{d-1}$

Dominik Barth

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Abstract

We use M\"uller and Nagy's method of contradicting subsets to give a new proof for the non-existence of sharply $2$-transitive subsets of the symplectic groups $\mathrm{Sp}(2d,2)$ in their doubly-transitive actions of degrees $2^{2d-1}\pm 2^{d-1}$. The original proof by Grundh\"ofer and M\"uller was rather complicated and used some results from modular representation theory, whereas our new proof requires only simple counting arguments.

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Dominik Barth. 2016-02-16. The non-existence of sharply $2$-transitive sets of permutations in $\mathrm{Sp}(2d,2)$ of degree $2^{2d-1} \pm 2^{d-1}$. https://doi.org/10.1007/s13366-016-0298-2

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