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• # Artykuł - szczegóły

## Acta Arithmetica

2014 | 165 | 2 | 123-140

## Quaternion extensions with restricted ramification

EN

### Abstrakty

EN
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 $p ≡ 1 (mod 2^{n-1})$, there exist unique real and complex normal number fields which are unramified outside S = {2,p} and cyclic over ℚ(√2) and whose Galois group is the (generalized) quaternion group $Q_{2^n}$ of order $2^n$.

123-140

wydano
2014

### Twórcy

autor
• Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany