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, 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
{\mathrm{Fi}_{24}^{\prime}}
by determining all
{(3,q,r)}
-generations, where q and r are prime divisors of
{\lvert\mathrm{Fi}_{24}^{\prime}\rvert}
with
{3<q<r}
.