Permutation groups and derangements of odd prime order

Timothy C. Burness; Michael Giudici

Permutation groups and derangements of odd prime order

Group Theory 2017-04-21 v2 Combinatorics

Authors: Timothy C. Burness , Michael Giudici

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.

Keywords

permutation groups derangements odd prime order quasiprimitive groups biquasiprimitive groups elusive groups arc-transitive graphs

Cite

@article{arxiv.1602.07617,
  title  = {Permutation groups and derangements of odd prime order},
  author = {Timothy C. Burness and Michael Giudici},
  journal= {arXiv preprint arXiv:1602.07617},
  year   = {2017}
}

Comments

21 pages; to appear in J. Combin. Theory Ser. A

Permutation groups and derangements of odd prime order

Abstract

Keywords

Cite

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