Emily Hall

Almost elusive groups

Let G be a transitive permutation group on a finite set X with |X|>1. A derangement in G is an element of G that has no fixed points on X, and as a consequence of the orbit-counting lemma we know that such elements always exist in G. But what happens if we seek derangements with special properties i.e specific order? In this talk I will discuss this question, with a special focus on derangements of prime order, and introduce the notion of almost elusive groups. I will provide motivation behind the concept of almost elusive groups and discuss key ideas lying behind the classification of these groups in the primitive setting.