The (p, q, r)-Generations of the Mathieu Group M22.

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|xl = ym = zn = 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 M22. GAP [16] and the Atlas of finite group representations [30] are used in our computations. [ABSTRACT FROM AUTHOR]