On the random generation of finite simple classical groups

摘要

Let G be a finite simple classical group with natural module of dimension n, and let r, s be primes, not both 2, with r less than or equal to s. Denote by P-r,P-s(G) the probability that G is generated by two randomly chosen elements of orders r and s. We prove that there is a quadratic function f such that if n greater than or equal to f (s), then P-r,P-s (G) --> 1 as G --> infinity.