2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66090In this Note we study the groups $G$ satisfying condition $(\mathcal{N},n)$, that is, every subset of $G$ with $n+1$ elements contains a pair $\{x,y\}$ such that the subgroup $<x,y>$ is nilpotent.Group Theory20F45;20F99text