ON EQUALITY OF ABSOLUTE CENTRAL AND CLASS PRESERVING AUTOMORPHISMS OF FINITE pGROUPS

Let $G$ be a finite nonabelian $p$group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite nonabelian $p$groups of order $p^n (nleq 5)$, for which every absolute central automorphism is class preserving.