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$x^{-1}{x}^{\alpha }\in G^{\prime }$ for all $x\in G$. The set of all$IA$-automorphisms of $G$ is denoted by $Au{t}^{G^{\prime }}(G)$. A group $G$is called semicomplete if and only if $Au{t}^{G^{\prime }}(G)=Inn(G)$. Inthis paper, we obtain certain conditions on a finite $p$-group tobe semicomplete.