Almost elusive permutation groups

Abstract

Let G be a transitive permutation group on a finite set Ω with |Ω| ⩾ 2. An element of G is said to be a derangement if it has no fixed points on Ω. As an easy consequence of the orbit counting lemma, G always contains such an element. In fact, by a theorem of Fein, Kantor and Schacher, G contains a derangement of prime power order. However, there do exist groups with no derangements of prime order; we call such groups elusive. As a natural extension, we say that G is almost elusive if it contains a unique conjugacy class of prime order derangements. In this thesis, we classify the quasiprimitive almost elusive groups.

Date of Award	3 Oct 2023
Original language	English
Awarding Institution	University of Bristol
Supervisor	Tim Burness (Supervisor)