Permutation groups and derangements of odd prime order

Tim Burness, Michael Giudici

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
240 Downloads (Pure)


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 20-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.
Original languageEnglish
Pages (from-to)102-130
Number of pages29
JournalJournal of Combinatorial Theory, Series A
Early online date5 May 2017
Publication statusPublished - Oct 2017


  • Derangement
  • Elusive group
  • Quasiprimitive group
  • Biquasiprimitive group
  • Arc-transitive graph

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