The S5 Extensions of Degree 6 with Minimum Discriminant
نویسندگان
چکیده
Research supported by the Natural Sciences and Engineering Research Council (Canada) and Fonds pour la Formation de Chercheurs et l'Aide a la Recherche (Qu ebec). The algebraic number fields of degree 6 having Galois group S5 and minimum discriminant are determined for signatures (0, 3), (2, 2) and (6, 0). The fields F0, F2, F6 are generated by roots of f0(t) = t 6 + 3t + 2t + 6t + 1, f2(t) = t 6 2t + 12t 16t + 8, and f6(t) = t 6 18t + 9t + 90t 70t 69 respectively. Each of these fields is unique up to isomorphism. This completes the enumeration of primitive sextic fields with minimum discriminant for all possible combinations of Galois group and signature.
منابع مشابه
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عنوان ژورنال:
- Experimental Mathematics
دوره 7 شماره
صفحات -
تاریخ انتشار 1998