ON THE Z_{l}-RANK OF ABELIAN EXTENSIONS WITH RESTRICTED RAMIFICATION

CHRISTIAN MAIRE

Abstract. For a prime number l, we consider l-extensions k_{S} of number fields k unramified outside a finite set S ⊂ S_{l} of places of k and, we study the ℤ_{l}- rank of the abelian part of k_{S}/k and the number of relations of the Galois group G_{S} := Gal(k_{S}/k).