# Invariable generation of finite classical groups

GRAW02 - Computational and algorithmic methods

We say a group is invariably generated by a subset if it forms a generating set even if an adversary is allowed to replace any elements with their conjugates. Eberhard, Ford and Green built upon the work of many others and showed that, as $n \rightarrow \infty$, the probability that $S_n$ is invariably generated by a random set of elements is bounded away from zero if there are four random elements, but goes to zero if we pick three random elements. This result gives rise to a nice Monte Carlo algorithm for computing Galois groups of polynomials. We will extend this result for $S_n$ to the finite classical groups using the correspondence between classes of maximal tori of classical groups and conjugacy classes of their Weyl groups.

This talk is part of the Isaac Newton Institute Seminar Series series.