  Two basic results on the S-rings over an abelian group are the Schur theorem
on multipliers and the Wielandt theorem on primitive S-rings over groups with a
cyclic Sylow subgroup. None of these theorems is directly generalized to the
non-abelian case. Nevertheless, we prove that they are true for the central
S-rings, i.e., for those which are contained in the center of the group ring of
the underlying group (such S-rings naturally arise in the supercharacter
theory). We also generalize the concept of a B-group introduced by Wielandt,
and show that any Camina group is a generalized B-group whereas with few
exceptions, no simple group is of this type.
