The Matrix Group Recognition Project

Already a group generated by two invertible $5\times 5$ matrices over a finite field can contain almost $10^7$ elements. It is therefore not surprising that many modern algorithms in Computational Group Theory are randomised.

This series of lectures provides a survey of modern algorithms to answer questions about matrix groups over finite fields and their complexity analysis. In many cases the analysis relies on good approximations of proportions of relevant elements in the groups considered.