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arXiv · 2601.20508

On the orbital diameter of classical groups in standard action

Attila Maróti·Kamilla Rekvényi
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Abstract

Let $G$ be a primitive permutation group acting on a finite set $X$. The orbital diameter $\mathrm{diam}(X,G)$ is defined to be the supremum of the diameters of the (connected) orbital graphs of $G$ after disregarding the directions of all edges in the graphs. This invariant is studied in the case when $G$ is an almost simple group in a standard action. A lower bound is given for $\mathrm{diam}(X,G)$ and we provide a partial classification of pairs $(X,G)$ for which the orbital diameter is at most $2$.

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Attila Maróti, Kamilla Rekvényi. 2026-01-28. On the orbital diameter of classical groups in standard action. https://arxiv.org/abs/2601.20508

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