Integrality of Stickelberger elements attached to unramified extensions of imaginary quadratic fields

In this paper, we prove the integrality of Stickelberger elements attached to finite (not necessarily abelian) unramified extensions of imaginary quadratic fields. As an application of this result, we describe the relation between non-commutative Fitting invariants of some arithmetic modules and Stickelberger elements. Consequently, we prove two types of annihilation results for ray class groups.