Abstract
A finite group G is called (l, m, n)-generated, if it is a quotient group of the triangle group T(l, m, n) = < x, y, z vertical bar x(l) = y(m) = z(n) = xyz = 1 >. In [24], Moori posed the question of finding all the ( p, q, r) triples, where p, q and r are prime numbers, such that a non-abelian finite simple group G is a (p, q, r)-generated. In this paper we will establish all the (p, q, r)-generations of the Mathieu group M-22. GAP [16] and the Atlas of finite group representations [30] are used in our computations.