### Abstract

A group G is said to be (l,m,n){(l,m,n)}-generated if it can be generated by two suitable elements x and y such that o(x)=l{o(x)=l}, o(y)=m{o(y)=m} and o(xy)=n{o(xy)=n}. In [J. Moori, (p,q,r){(p,q,r)}-generations for the Janko groups J1{J_{1}} and J2{J_{2}}, Nova J. Algebra Geom. 2 1993, 3, 277–285], J. Moori posed the problem of finding all triples of distinct primes (p,q,r){(p,q,r)} for which a finite non-abelian simple group is (p,q,r){(p,q,r)}-generated. In the present article, we partially answer this question for Fischer’s largest sporadic simple group Fi24′{\mathrm{Fi}_{24}^{\prime}} by determining all (3,q,r){(3,q,r)}-generations, where q and r are prime divisors of |Fi24′|{\lvert\mathrm{Fi}_{24}^{\prime}\rvert} with 3<q<r{3<q<r}.