On Finite Groups with Isomorphic Centers of Group Rings

Let G and H be two finite groups,R is the ring of all the algebraic integers in the field C of complex numbers.Denote the group algebra of G over R by RG and the central of RG by Z(RG).In this note,the following question is discussed: Suppose that Z(RG)≌Z(RH),then H is not necessarily an inner nilpotent group if G is an inner nilpotent group.Furthermore,the structure of the finite group H can be obtained.