Pure Maths Colloquium: Scott Harper

By a classical theorem of Jordan, every nontrivial finite group acting transitively on a set contains a derangement (an element with no fixed points). Much more is now known, especially in the context of (almost) simple groups. In this talk, I’ll discuss some strong versions of this result and some applications. I’ll then focus on the question of whether there exist almost simple groups with elements that are derangements in every faithful primitive action, and I’ll show how this solves a question of Garzoni about invariable generating sets for simple groups.