@article {
author = {Abdollahi, Alireza and Ghoraishi, S. Mohsen},
title = {Noninner automorphisms of finite p-groups leaving the center elementwise fixed},
journal = {International Journal of Group Theory},
volume = {2},
number = {4},
pages = {17-20},
year = {2013},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2013.2761},
abstract = {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.},
keywords = {Noninner automorphism,finite p-groups,the center},
url = {https://ijgt.ui.ac.ir/article_2761.html},
eprint = {https://ijgt.ui.ac.ir/article_2761_52bac5d4d3e407efd00cc7724a0d360e.pdf}
}