COMPUTING THE TORSION OF THE p-RAMIFIED MODULE OF A NUMBER FIELD

We fix a prime number p and a number field K, and denote by M the maximal abelian p-extension of K unramified outside p. Our aim is to study the Z(p)-module x = Gal(M/K) and to give a method to effectively compute its structure as a Z(p)-module. We also give numerical results, for real quadratic fields, cubic fields and quintic fields, together with their interpretations via Cohen-Lenstra heuristics.