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arXiv · 1602.07617

Permutation groups and derangements of odd prime order

Timothy C. Burness·Michael Giudici
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Abstract

Let $G$ be a transitive permutation group of degree $n$. We say that $G$ is $2'$-elusive if $n$ is divisible by an odd prime, but $G$ does not contain a derangement of odd prime order. In this paper we study the structure of quasiprimitive and biquasiprimitive $2'$-elusive permutation groups, extending earlier work of Giudici and Xu on elusive groups. As an application, we use our results to investigate automorphisms of finite arc-transitive graphs of prime valency.

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Timothy C. Burness, Michael Giudici. 2016-02-24. Permutation groups and derangements of odd prime order. https://arxiv.org/abs/1602.07617

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