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arXiv · 2110.07896

On primitive $2$-closed permutation groups of rank at most four

Michael Giudici·Luke Morgan·Jin-Xin Zhou
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Abstract

We characterise the primitive 2-closed groups $G$ of rank at most four that are not the automorphism group of a graph or digraph and show that if the degree is at least 2402 then there are just two infinite families or $G\leqslant \mathrm{A}Γ\mathrm{L}_1(p^d)$, the 1-dimensional affine semilinear group. These are the first known examples of non-regular 2-closed groups that are not the automorphism group of a graph or digraph.

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Michael Giudici, Luke Morgan, Jin-Xin Zhou. 2022-09-17. On primitive $2$-closed permutation groups of rank at most four. https://arxiv.org/abs/2110.07896

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