2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98862We give elementary applications of quasi-homomorphisms to growth problems in groups. A particular case concerns the number of torsion elements required to factorise a given element in the mapping class group of a surface.Revised to include a discussion of weak bounded generation, both in general and for mapping class groups; now 8 pagesGroup TheoryGeometric Topologyprimary 20F69, secondary 20F12, 57M07text