18.117 (2014)

Is every element of a nonabelian finite simple group a commutator of two elements of coprime orders?

The answer is known to be “yes” for the alternating groups (P. Shumyatsky, Forum Math., 27, no. 1 (2015), 575–583) and for $\text{PSL}(2, q)$ (M. A. Pellegrini, P. Shumyatsky, Arch. Math., 99 (2012), 501–507). Without the coprimeness condition, this is Ore’s conjecture proved in (M. W. Liebeck, E. A. O’Brien, A. Shalev, Pham Huu Tiep, J. Eur. Math. Soc., 12, no. 4 (2010), 939–1008).