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

Faryad Ali, Mohammed Ali Faya Ibrahim, Andrew Woldar
2019 Journal of group theroy  
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
more » ... 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} .
doi:10.1515/jgth-2018-0104 fatcat:rlujbj2c75d3vhkomx6ya3r5m4