(p,q,r)-Generations and nX-Complementary Generations of the Thompson Group Th

A group G is said to be (l, m, n)-generated if it is a quotient group of the triangle group T (l, m, n) = x, y, z|x l = y m = z n = xyz = 1 .In 1993 J. Moori posed the question of finding all triples (l, m, n) such that a given non-abelian finite simple group is (l, m, n)-generated.In this paper we partially answer this question for the Thompson group T h.In fact we study (p, q, r)-generation, where p, q and r are distinct primes, and nX-complementary generations of the Thompson group T h.