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arXiv · 2301.05569

The quasiprimitive almost elusive groups

Emily V. Hall
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Abstract

Let $G$ be a nontrivial transitive permutation group on a finite set $\Omega$ and recall that an element of $G$ is a derangement if it has no fixed points. Derangements always exist by a classical theorem of Jordan, but there are so-called elusive groups that do not contain any derangements of prime order. In a recent paper, Burness and the author introduced the family of almost elusive groups, which contain a unique conjugacy class of derangements of prime order. In this paper, we complete the classification of the quasiprimitive almost elusive groups.

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Emily V. Hall. 2023-01-13. The quasiprimitive almost elusive groups. https://arxiv.org/abs/2301.05569

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