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| Subgroups of Class Groups of Algebraic Quadratic Function Fields |
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Citation： |
WANG Kunpeng,ZHANG Xianke.Subgroups of Class Groups of Algebraic Quadratic Function Fields[J].Chinese Annals of Mathematics B,2003,24(3):315~322 |
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Net amount： 755 |
Authors： |
WANG Kunpeng; ZHANG Xianke |
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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 $n$. |
Keywords： |
Function field, Quadratic extension, Class group, Class number, Continued fraction |
Classification： |
11R11, 11R29, 11R58, 14H05 |
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