| SUBGROUPS OF CLASS GROUPS OF ALGEBRAIC QUADRATIC FUNCTION FIELDS |
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| 引用本文： | WANG Kunpeng,ZHANG Xianke. SUBGROUPS OF CLASS GROUPS OF ALGEBRAIC QUADRATIC FUNCTION FIELDS[J]. 数学年刊B辑(英文版), 2003, 24(3): 315-322 |
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| 作者姓名： | WANG Kunpeng ZHANG Xianke |
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| 作者单位： | WANG KUNPENG ZHANG XIANKE State Key Laboratory of Information Security，Graduate School of Chinese Academy of Sciences，Beijing100039，China. Department of Mathematical Sciences，Tsinghua University，Beijing 100084，China. |
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| 摘 要： | Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, which holds true for both real and imaginary fields K. Then several series of function fields K, including real, inertia imaginary, and ramified imaginary quadratic function fields, are given, for which the class groups H(K) are proved to contain cyclic subgroups of order n.
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| 关 键 词： | 子群 类群 函数域 二次扩张 类数 正常解 连分式 Diophantine方程 |
| 收稿时间： | 2008-04-02 |
Subgroups of Class Groups of Algebraic Quadratic Function Fields |
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| WANG Kunpeng and ZHANG Xianke. Subgroups of Class Groups of Algebraic Quadratic Function Fields[J]. Chinese Annals of Mathematics,Series B, 2003, 24(3): 315-322 |
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| Authors: | WANG Kunpeng and ZHANG Xianke |
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| Affiliation: | 1. State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences, Beijing 100039, China
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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| Abstract: | Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, which holds true for both real and imaginary fields K. Then several series of function fields K, including real, inertia imaginary, and ramified imaginary quadratic function fields, are given, for which the class groups H(K) are proved to contain cyclic subgroups of order n. |
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| Keywords: | Function field Quadratic extension Class group Class number Continued fraction |
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