On Automorphisms of Finite $p$-groups

Abstract

Let $G$ be a finite $p$-group such that $x\mathbb{Z}(G)\subseteq x^G$ for all $x\in G-\mathbb{Z}(G)$, 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 Theory

References in corpus (1)

• Class Preserving Automorphisms of Finite p-groups