2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146794Let $G$ be a finite $p$-group such that $x\Z(G) \subseteq x^G$ for all $x \in G- \Z(G)$, where $x^G$ denotes the conjugacy class of $x$ in $G$. Then $|G|$ divides $|\Aut(G)|$, where $\Aut(G)$ is the group of all automorphisms of $G$.Appeared in Journal of Group TheoryGroup Theory20D45; 20D15text