Annihilation of Selmer groups for monomial CM-extensions

Let F/k be a finite Galois extension of number fields with Galois group G, and A an abelian variety over k. We fix an odd prime p. When G is isomorphic to the dihedral group of order 4p, assuming the Birch and Swinnerton-Dyer conjecture and some technical assumptions, we prove that the Pontryagin dual of the (classical) Selmer group Selp(AF)∨ is annihilated by some element in the center of the group ring Zp[G] which is constructed from equivariant L-values. More generally, we study the relation between the annihilation of Selmer groups for non-abelian extensions and that for abelian extensions.