2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112942We establish correspondances between factorisations of finite abelian groups (direct factors, unitary factors, non isomorphic subgroup classes) and factorisations of integer matrices. We then study counting functions associated to these factorisations and find average orders.18 pages, v2: Clarified definition 4. Changed "without zeroes" to "without real zeroes" at five placesNumber TheoryCombinatorics11M41; 20K01; 15A36text