on equality of absolute central and class preserving automorphisms of finite p-groups

Abstract. let g be a finite non-abelian p-group and l(g) de- notes the absolute center of g. also, let autl(g) and autc(g) denote the group of all absolute central and the class preserving au- tomorphisms of g, respectively. in this paper, we give a necessary and sufficient condition for g such that autc(g) = aut^l(g). we also characterize all finite non-abelian p-groups of order p^n(n ≤ 5), for which every absolute central automorphism is class preserving.