2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99966A group is called capable if it is a central factor group. We consider the capability of nilpotent products of cyclic groups, and obtain a generalization of a theorem of Baer for the metabelian small class case. The approach is also used to obtain some recent results on the capability of certain nilpotent groups of class 2. We also prove a necessary condition for the capability of an arbitrary p-group of class k, and some further results.Errata updated; the error can be fixed, and a correct proof will appear in a part 2Group Theory20D15, 20F12 (Primary)text