Abstract :
LetF/kbe an abelian extension, with some conditions of signature forkandF, and letpbe a prime number not dividing [F : k]. We prove, essentially, that there exists (infinitely many)p-extensionsKofF, abelian overk, such that thep-class groupClFofFbecomes trivial inK. These extensionsK/Fare effectively known and the structure of the group Gal(K/F) is directly connected with that ofClF. Numerical examples are given.
