On the nilpotency class of the automorphism group of some finite p-groups

Document Type : Research Paper



Let $G$ be a $p$-group of order $p^n$ and $Phi$=$Phi(G)$ be the
Frattini subgroup of $G$. It is shown that the nilpotency class of
$Autf(G)$, the group of all automorphisms of $G$ centralizing $G/
Fr(G)$, takes the maximum value $n-2$ if and only if $G$ is of
maximal class. We also determine the nilpotency class of
$Autf(G)$ when $G$ is a finite abelian $p$-group.


Volume 37, No. 3
September 2011
Pages 281-289
  • Receive Date: 18 January 2010
  • Revise Date: 15 March 2012
  • Accept Date: 04 April 2010
  • First Publish Date: 15 September 2011