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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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