ℚ of galois 2-extensions
✍ Scribed by Helen G. Grundman; David B. Leep; Tara L. Smith
- Book ID
- 110672292
- Publisher
- The Hebrew University Magnes Press
- Year
- 2002
- Tongue
- English
- Weight
- 351 KB
- Volume
- 130
- Category
- Article
- ISSN
- 0021-2172
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We classify quadratic, biquadratic and degree 4 cyclic 2-rational number fields. We also classify those quadratic number fields which are not 2-rational, but have a degree 2 extension, which is Galois over Q and is 2-rational. In this case we explicitly describe the Galois group of their maximal pro
Let k be a Galois extension of Q with [k : Q]=d 2. The purpose of this paper is to give an upper bound for the least prime which does not split completely in k in terms of the degree d and the discriminant 2 k . Our estimate improves on the bound given by Lagarias et al. [3]. We note, however, that