On (p, q, r)-generations of the Tits group

A finite group G is called (l, m, n)-generated if it is generated by two elements x and y, such that the orders of x, y, and xy are l, m, and n, respectively.A triple (p, q, r) is called (p, q, r)-generation of a group G if G is (p, q, r)-generated.In [Nova J. Algebra Geom. 2 (1993) 277-285], Moori posed the question of finding all (p, q, r)-generations of non-abelian finite simple groups such that p, q, and r are prime numbers.In answering this question, we determine all (p, q, r)-generations of the Tits group 2 F4(2) , where p, q, and r are prime numbers dividing the order of this group.We primarily use the structure constant method, along with other results, to establish the generation and non-generation of 2 F4(2) by triples (p, q, r).We use the GAP (Groups, Algorithms and Programming) system and the Atlas of Finite Group Representations in our computations.