  An $S$-ring (Schur ring) is called central if it is contained in the center
of the group ring. We introduce the notion of a generalized Schur group, i.e.
such finite group that all central $S$-rings over this group are schurian. It
generalizes in a natural way the notion of a Schur group and they are
equivalent for abelian groups. We establish basic properties and provide
infinite families of nonabelian generalized Schur groups
