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

Document Type : Research Paper

Authors

Abstract

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.

Keywords

### History

• Receive Date: 18 January 2010
• Revise Date: 15 March 2012
• Accept Date: 04 April 2010
• First Publish Date: 15 September 2011