The Schur group of an abelian number field

We characterize the maximum rr-local index of a Schur algebra over an abelian number field KK in terms of global information determined by the field KK for an arbitrary rational prime, rr. This completes and unifies previous results of Janusz in [G.J. Janusz, The Schur group of an algebraic number field, Ann. of Math. (2) 103 (1976) 253–281] and Pendergrass in [J.W. Pendergrass, The 2-part of the Schur group, J. Algebra 41 (1976) 422–438].