A note on automorphisms of finite $p$-groups

Gustavo A. Fernández-Alcober, Anitha Thillaisundaram

Let $G$ be a finite non-cyclic $p$-group of order at least $p^3$. If $G$ has an abelian maximal subgroup, or if $G$ has an elementary abelian centre with $C_G(Z(\Phi (G)))\ne \Phi (G)$, t…