The quasiprimitive almost elusive groups

2023/01/13 by Emily V. Hall, Hall, Emily V. · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2301.05569

openalex publication_date 2023/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a nontrivial transitive permutation group on a finite set Ω 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.

Cited by

• Elusive groups from non-split extensions

Related

• Almost elusive permutation groups
• Almost elusive classical groups
• Permutation groups and derangements of odd prime order
• Locally elusive classical groups
• Elusive groups from non-split extensions