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Zbl 0601.12013
Kwon, S.-H.; Martinet, J.
Sur les corps résolubles de degré premier. (On soluble fields of prime degree).
(French)
[J] J. Reine Angew. Math. 375/376, 12-23 (1987). ISSN 0075-4102; ISSN 1435-5345/e

Let K be a soluble number field of prime degree $\ell$. For such a field, the Galois closure is of degree m over ${\bbfQ}$ for some m dividing $\ell -1$. The smallest discriminants are determind for some pairs ($\ell,m)$, including all cases with $\ell \le 7$ except (7,6) in the totally real case. Some polynomials are given for $\ell \le 5$. The results are obtained by combining class field theory and Kummer theory.
MSC 2000:
*11R21 Other number fields
11R37 Class field theory for global fields
11R23 Iwasawa theory

Keywords: soluble number field; smallest discriminants; class field theory; Kummer theory

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