We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We settle the noninner automorphism conjecture for finite p-groups (
$p> 2$) with certain conditions. Also, we give an elementary and short proof of the main result of Ghoraishi [‘On noninner automorphisms of finite nonabelian p-groups’, Bull. Aust. Math. Soc. 89(2) (2014) 202–209].
Let 
$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G$ be a finite 2-group. If 
$G$ is of coclass 2 or 
$(G,Z(G))$ is a Camina pair, then 
$G$ admits a noninner automorphism of order 2 or 4 leaving the Frattini subgroup elementwise fixed.
