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) =. T (l, m, n) = x, y, z | x l = y m = z n = x y z = 1. In 23, Moori posed the question of finding all the (p, q, r) triples, where p, \ q p, q and r are prime numbers, such that a non-abelian finite simple group G is a (p, q, r) -generated. In answering this question, we establish all the (p, q, r) -generations for the group G₂ (3). G 2 (3). We mainly used the structure constant method together with other results to establish the generation and non-generation of the G₂ (3) G 2 (3) by the triples (p, q, r). The Groups, Algorithms and Programming, GAP 21 and the Atlas of finite group representations 27 are used in our computations.
Basheer et al. (2026) studied this question.