It has been shown by Madden that there are only finitely many quadratic extensions of k(x), k a finite field, in which the ideal class group has exponent two and the infinity place of k(x) ramifies. We give a characterization of such fields that allow us to find a full list of all such field extensi
On imaginary quadratic function fields with the ideal class group to be exponent ≤2
✍ Scribed by Weiqun Hu
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 467 KB
- Volume
- 43
- Category
- Article
- ISSN
- 1001-6538
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📜 SIMILAR VOLUMES
Focusing on a particular case, we will show that one can explicitly determine the quartic fields \(\mathbf{K}\) that have ideal class groups of exponent \(\leqslant 2\), provided that \(\mathbf{K} / \mathbf{Q}\) is not normal, provided that \(\mathbf{K}\) is a quadratic extension of a fixed imaginar
Let k be an imaginary quadratic number field with C k, 2 , the 2-Sylow subgroup of its ideal class group, isomorphic to ZÂ2Z\_ZÂ2Z\_ZÂ2Z. By the use of various versions of the Kuroda class number formula, we improve significantly upon our previous lower bound for |C k 1 , 2 | , the 2-class number of