TY - JOUR
ID - 2761
TI - Noninner automorphisms of finite p-groups leaving the center elementwise fixed
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Abdollahi, Alireza
AU - Ghoraishi, S. Mohsen
AD - University of Isfahan
Y1 - 2013
PY - 2013
VL - 2
IS - 4
SP - 17
EP - 20
KW - Noninner automorphism
KW - finite p-groups
KW - the center
DO - 10.22108/ijgt.2013.2761
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_2761.html
L1 - https://ijgt.ui.ac.ir/article_2761_52bac5d4d3e407efd00cc7724a0d360e.pdf
ER -