A subset X of a group G invariably generates G if we are free to replace each element of X by an arbitrary conjugate, and we must always obtain a generating set of G. This concept was introduced by Dixon in the early nineties with motivations from computational Galois theory. We will review these motivations and their intimate connections with permutation groups.
We will then present some new results concerning the probability of generating invariably a finite simple group. For instance, we will see that two random elements of a finite simple group of Lie type of bounded rank invariably generate with probability bounded away from zero.
Joint work with Eilidh McKemmie.
This video was produced by Tel Aviv University as part of its algebra seminar.
