Non-cyclic class groups and the Brumer–Stark conjecture

For an odd prime number p, we consider the p-primary part of the Brumer–Stark conjecture for a cyclic extension K/k of number fields of degree 2p. We extend earlier work of Greither, Roblot, and Tangedal (2004) [4] by proving the conjecture when the minus component of the p-primary part of the class group of K is not a cyclic Galois module. Consequently, we are able to prove the full Brumer–Stark conjecture for some new classes of number field extensions.