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Galois extensions of prime degree

โœ Scribed by Cornelius Greither; Rick Miranda

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
637 KB
Volume
124
Category
Article
ISSN
0021-8693

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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

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Let p be an odd prime and n a positive integer and let k be a field of ลฝ . r p and let r denote the largest integer between 0 and n such that K l k s p ลฝ . r r r k , where denotes a primitive p th root of unity. The extension Krk is p p separable, but not necessarily normal and, by Greither and Pa