Shahrood University of TechnologyJournal of Algebraic Systems2345-51286220190101On equality of absolute central and class preserving automorphisms of finite $p$-groups147155136410.22044/jas.2018.6849.1335ENRasoul SoleimaniDepartment of Mathematics, Payame Noor University (PNU), P.O.Box 19395-3697,
Tehran, Iran.Journal Article20180311Let $G$ 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 $p^n (nleq 5)$, for which every absolute central automorphism is class preserving.<br /><br />http://jas.shahroodut.ac.ir/article_1364_aff3c1c2ba782919ee62a881ce5926c0.pdf