  We define a Schur-Clifford subgroup of Turull's Brauer-Clifford group,
similar to the Schur subgroup of the Brauer group. The Schur-Clifford subgroup
contains exactly the equivalence classes coming from the intended application
to Clifford theory of finite groups. We show that the Schur-Clifford subgroup
is indeed a subgroup of the Brauer-Clifford group, as are certain naturally
defined subsets. We also show that this Schur-Clifford subgroup behaves well
with respect to restriction and corestriction maps between Brauer-Clifford
groups.
