Generating Pairs for the Fischer Group Fi23.

A group G is said to be (l, m, n)-generated if it is a quotient of the triangle group T (l , m , n) = ⟨ x , y , z ∣ x l = y m = z n = x y z = 1 ⟩. Moori posed in 1993 the question of finding all the triples (l, m, n) such that non-abelian finite simple groups are (l, m, n)-generated. We partially answer this question for the Fischer sporadic simple group Fi₂₃. In particular, we investigate all (2, q, r)-generations for the Fischer sporadic simple group Fi₂₃, where q and r are distinct prime divisors of |Fi₂₃|. [ABSTRACT FROM AUTHOR]