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Sur les corps résolubles de degré premier. (On soluble fields of prime degree). (French) Zbl 0601.12013

Let K be a soluble number field of prime degree \(\ell\). For such a field, the Galois closure is of degree m over \({\mathbb{Q}}\) for some m dividing \(\ell -1\). The smallest discriminants are determind for some pairs (\(\ell,m)\), including all cases with \(\ell \leq 7\) except (7,6) in the totally real case. Some polynomials are given for \(\ell \leq 5\). The results are obtained by combining class field theory and Kummer theory.

MSC:

11R21 Other number fields
11R37 Class field theory
11R23 Iwasawa theory
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