2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/227376Let G be a finite group, p a fixed prime and P a Sylow p-subgroup of G. In this short note we prove that if p is odd, G is p-nilpotent if and only if P controls fusion of cyclic groups of order p. For the case p=2, we show that G is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and 4.7 pagesGroup Theory20D15; 20J06text