Construction de la tour des 2-corps de classes de Hilbert de certains corps biquadratiques

@inproceedings{Azizi2003ConstructionDL,
  title={Construction de la tour des 2-corps de classes de Hilbert de certains corps biquadratiques},
  author={Abdelmalek Azizi},
  year={2003}
}
Let p and q be prime numbers such that p ≡ 1 mod 8, q ≡ -1 mod 4 and () = -1, d = pq, k = Q(d,i), k (1) 2 be the 2-Hilbert class field of k, k (2) 2 be the 2-Hilbert class field of k (1) 2 and G 2 be the Galois group of k (2) 2 /k. The 2-part C k,2 of the class group of k is of type (2, 2), so k (1) 2 contains three extensions K i /k, i = 1, 2, 3. Our goal is to determine the group C k,2 , to study the problem of capitulation of the 2-classes of k in K i , i = 1, 2, 3 and to construct the 2… CONTINUE READING