%0 Journal Article
%T Noninner automorphisms of finite p-groups leaving the center elementwise fixed
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Abdollahi, Alireza
%A Ghoraishi, S. Mohsen
%D 2013
%\ 12/01/2013
%V 2
%N 4
%P 17-20
%! Noninner automorphisms of finite p-groups leaving the center elementwise fixed
%K Noninner automorphism
%K finite p-groups
%K the center
%R 10.22108/ijgt.2013.2761
%X A 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.
%U https://ijgt.ui.ac.ir/article_2761_52bac5d4d3e407efd00cc7724a0d360e.pdf