The (p, q, r)-generations of the alternating group A10

A finite 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|xl = ym = zn = xyz = 1. In 28, 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 (p, q, r)-generated. In this paper we will establish all the (p, q, r)-generations of the alternating group A10. GAP 24 and the Atlas of finite group representations 1 are used in our computations.