학술저널
THAINE’S THEOREM IN FUNCTION FIELD
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 22, No. 1
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2009.0317 - 23 (7 pages)
- 0
Let F be a finite real abelian extension of a global function field k with G = Gal(F/k). Assume that F is an extension field of the Hilbert class field Ke of k and is contained in a cyclotomic function field Kn. Let ` be any prime number not dividing phk|G|. In this paper, we show that if 2 Z[G] annihilates the Sylow `-subgroup of O×F /CF, then (q−1) annihilates the Sylow `-subgroup of ClF.
1. Introduction
2. Preliminary
3. Proof of Theorem 1.1
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