some new properties of autocentral automorphism group

Let g be a group, aut(g) and l(g) denote the full automorphisms group and absolutecenter of g, respectively. an automorphism α ∈ aut(g) is called autocentral automorphismif g−1α(g) ∈ l(g), for all g ∈ g. in this article, we study some new properties of autocentralautomorphisms of given group g. we identify the elements of a group that are fixed by anyautocentaral automorphism of group and introduce the autocentral kernel of a group g. autocentralkernel of a given group is a generalizition of central kernel which was studied by f.haimo in 1995.