University of IsfahanInternational Journal of Group Theory2251-76502420131201Noninner automorphisms of finite p-groups leaving the center elementwise fixed1720276110.22108/ijgt.2013.2761ENAlirezaAbdollahiUniversity of Isfahan0000-0001-7277-4855S. MohsenGhoraishiUniversity of IsfahanJournal Article20130225A longstanding conjecture asserts that every finite nonabelian $p$-group admits a noninner automorphism of order $p$. Let $G$ be a finite nonabelian $p$-group. It is known that if $G$ is regular or of nilpotency class $2$ or the commutator subgroup of $G$ is cyclic, or $G/Z(G)$ is powerful, then $G$ has a noninner automorphism of order $p$ leaving either the center $Z(G)$ or the Frattini subgroup $\Phi(G)$ of $G$ elementwise fixed. In this note, we prove that the latter noninner automorphism can be chosen so that it leaves $Z(G)$ elementwise fixed.https://ijgt.ui.ac.ir/article_2761_52bac5d4d3e407efd00cc7724a0d360e.pdf