Classes réalisables par des extensions métacycliques non abéliennes et éléments de Stickelberger Original Research Article

Letkbe a number field,Okits ring of integers,Γa nonabelian metacyclic group of orderlq, wherel,qare prime numbers. Assume thatkand thelqth cyclotomic field of image are linearly disjoint over image. Let image be a maximalOk-order ink[1] containingOk[Γ],image(image) its class group. We determine the set of elements ofimage(image) which are realizable by some tamely ramified extensions with Galois groups isomorphic toΓusing some Stickelberger elements, and we prove that it is a subgroup ofimage(image).