(3, 𝑞, 𝑟)-generations of Fischer's sporadic group Fi′24.

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 J₁ and J₂, Nova J. Algebra Geom. 2 1993, 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 |Fi′₂₄| with 3 < q < r. [ABSTRACT FROM AUTHOR]