2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67961Let Mod_{g,b} denote the mapping class group of a surface of genus g with b punctures. Feng Luo asked in a recent preprint if there is a universal upper bound, independent of genus, for the number of torsion elements needed to generate Mod_{g,b}. We answer Luo's question by proving that 3 torsion elements suffice to generate Mod_{g,0}. We also prove the more delicate result that there is an upper bound, independent of genus, not only for the number of torsion elements needed to generate Mod_{g,b} but also for the order of those elements. In particular, our main result is that 6 involutions (i.e. orientation-preserving diffeomorphisms of order two) suffice to generate Mod_{g,b} for every genus g >= 3, b = 0, and g >= 4, b = 1.15 pages, 7 figures; slightly improved main result; minor revisions. to appear in J. AlgGeometric TopologyGroup Theory20F65 (Primary) 57M07, 20F38 (Secondary)text