Generating Pairs for the Fischer Group Fi23

Abstract

A group G is said to be (l, m, n)-generated if it is a quotient of the triangle group [Formula: see text]. 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|.