%0 Journal Article %T ON EQUALITY OF ABSOLUTE CENTRAL AND CLASS PRESERVING AUTOMORPHISMS OF FINITE p-GROUPS %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Soleimani, Rasoul %D 2019 %\ 01/01/2019 %V 6 %N 2 %P 147-155 %! ON EQUALITY OF ABSOLUTE CENTRAL AND CLASS PRESERVING AUTOMORPHISMS OF FINITE p-GROUPS %K Automorphism group %K Absolute centre %K Finite p-group %R 10.22044/jas.2018.6849.1335 %X Let $G$ be a finite non-abelian $p$-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 non-abelian $p$-groups of order $p^n (n\leq 5)$, for which every absolute central automorphism is class preserving. %U https://jas.shahroodut.ac.ir/article_1364_aff3c1c2ba782919ee62a881ce5926c0.pdf