Abstract
A group G is said to be (l, m, n)-generated if it can be generated by two suitable elements x and y such that o(x) = l, o(y) = m and o(xy) = n. In [J. Moori, (p, q, r)-generations for the Janko groups J 1 and J 2, Nova J. Algebra Geom. 2 (1993), no. 3, 277-285], J. Moori posed the problem of finding all triples of distinct primes (p, q, r) for which a finite non-abelian simple group is (p, q, r)-generated. In the present article, we partially answer this question for Fischer's largest sporadic simple group Fi'(24) by determining all (3, q, r)-generations, where q and r are prime divisors of vertical bar Fi'(24)vertical bar with 3 < q < r.