Chapter 2 Estimation Problems and Randomised Group Algorithms

In 1973, Charles Sims [89] proved the existence of the Lyons–Sims sporadic simple group Ly by constructing its action as a group of permutations of a set of cardinality 8,835,156 on a computer which could not even store and multiply the two generators of Ly in this smallest degree permutation representation for the group! The existence of this finite simple group, together with many of its properties, had been predicted by Richard Lyons [60], but proof of existence was not established until Sims’ construction. Leading up to this seminal achievement, Sims [88] had developed concepts and computational methods that laid the foundation for his general theory of permutation group computation.