Subgroups of class groups of algebraic quadratic function fields

被引：0

作者：

Wang, KP ^{[1
]}

Zhang, XK

机构：

[1] Acad Sinica, Grad Sch, State Key Lab Informat Secur, Beijing 100039, Peoples R China

[2] Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2003年 / 24卷 / 03期

关键词：

function field; quadratic extension; class group; class number; continued fraction;

D O I：

10.1142/S0252959903000311

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：315 / 322

页数：8

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