Shahrood University of Technology Journal of Algebraic Systems 2345-5128 3 2 2015 01 01 ON ABSOLUTE CENTRAL AUTOMORPHISMS FIXING THE CENTER ELEMENTWISE 127 131 612 10.22044/jas.2015.612 EN Z. Kaboutari Farimani Department of Mathematics, University of Birjand, Birjand, Iran. M. M. Nasrabadi Department of Mathematics, University of Birjand, Birjand, Iran. Journal Article 2015 02 28 Let G be a finite p-group and let Aut_l(G) be the group of absolute central automorphisms of G. In this paper we give necessary and sufficient condition on G such that each absolute central automorphism of G fixes the centre element-wise. Also we classify all groups of orders p^3 and p^4 whose absolute central automorphisms fix the centre element-wise. https://jas.shahroodut.ac.ir/article_612_1811e3d5e5fb09d4b5f4e6ce4fb36612.pdf