Permutation groups and derangements of odd prime order

2016/02/24 by Burness, Timothy C., Giudici, Michael
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1602.07617

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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• Almost elusive classical groups
• The quasiprimitive almost elusive groups
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• An infinite family of counterexamples to the Polycirculant Conjecture