18.98 (2014)

The work of many authors shows that most finite simple groups are generated by two elements of orders 2 and 3; for example, see the survey. Which finite simple groups cannot be generated by two elements of orders 2 and 3? In particular, is it true that, among classical simple groups of Lie type, such exceptions, apart from $\text{PSU}(3, 5^2)$, arise only when the characteristic is 2 or 3?

The question of which finite simple groups are (2,3)-generated remains open only for the orthogonal groups of even dimension $2m > 8$ (M. A. Pellegrini, M. C. Tamburini Bellani, J. Austral. Math. Soc., 117 (2024), 130–148).