For any group G, let C(G) denote the intersection of the normalizers of centralizers of all elements of G. Set C0 = 1. De ne Ci+1(G)=Ci(G) = C(G=Ci(G)) for i 0. Denote by C1(G) the terminal term of this ascending series. We show that a nitely generated group G is nilpotent if and only if G = Cn(G) for some positive integer n.
