2000 Mathematics Subject Classification: 12F12We describe several types of Galois extensions having as Galois group the quaternion group Q16 of order 16.This work is partially supported by project of Shumen University.

In any normal number field having Q₈, the quaternion group of order 8, as Galois group over the rationals, at least two finite primes must ramify. The classical example by Dedekind of such a field is extraordinary in that it is totally real and only the primes 2 and 3 are ramified. In this note we describe in detail all Q₈-fields over the rationals where only two (finite) primes are ramified. We also show that, for any integer n>3 and any prime $p\equiv 1\left(mod{2}^{n-1}\right)$, there exist unique real and complex normal number...

On étudie différentes propriétés d’approximation pour des espaces homogènes $X$ (à stabilisateur fini) de ${\mathrm{GL}}_n$ sur un corps de nombres. On discute également du lien avec le problème de Galois inverse et on établit une formule pour le groupe de Brauer non ramifié de $X$.