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arXiv · 2304.08459

On transitive sets of derangements in primitive groups

Peter Müller
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Abstract

We construct a primitive permutation action of the Steinberg triality group $^3D_4(2)$ of degree $4064256$ and show that there are distinct points $\alpha,\beta$ such that there is no derangement $g\in{^3D_4}(2)$ with $\alpha^g=\beta$. This answers a question by John G. Thompson (Problem 8.75 in the Kourovka Notebook) in the negative.

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Peter Müller. 2023-04-17. On transitive sets of derangements in primitive groups. https://doi.org/10.1007/s00013-026-02240-3

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