A note on $IA$-automorphisms of a finite $p$-group

Abstract

Let $G$ be a finite group. Anautomorphism $\alpha$ of $G$ is called an $IA$-auto\-mor\-phism if$x^{-1}x^{\alpha}\in G'$ for all $x\in G$. The set of all$IA$-automorphisms of $G$ is denoted by $Aut^{G'}(G)$. A group $G$is called semicomplete if and only if $Aut^{G'}(G)=Inn(G)$. Inthis paper, we obtain certain conditions on a finite $p$-group tobe semicomplete.