| 关于Q(4k~(2n)+1)的理想类群的循环子群 |
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| 引用本文： | 陈宏基.关于Q(4k~(2n)+1)的理想类群的循环子群[J].数学学报,1999,42(6):0. |
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| 作者姓名： | 陈宏基 |
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| 作者单位： | 惠州大学数学系!惠州５１６０１５ |
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| 摘 要： | 设ｄ，ａ，ｋ，ｎ是适合４ｋ２ｎ＋１＝ｄａ２，ｋ＞１，ｎ＞２，ｄ无平方因子的正整数；又设Ｃ（Ｋ）和ｈ（Ｋ）分别是实二次域Ｋ的理想类群和类数．本文证明了：当ａ＜０．５ｋ０．５６ｎ时，则ｈ（ｋ）＝０（ｍｏｄｎ）和Ｃ（Ｋ）必有ｎ阶循环子群．
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| 关 键 词： | 实二次域 理想类群 循环子群 类数 可除性 |
On the Cyclic Subgroups of the Ideal Class Group of Q(4k~(2n)+1) |
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| Institution: | Chen Hongji(Department of Mathematics, Huizhou University, Huizhou 516015, P. R. China) |
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| Abstract: | Let d, a, k, n be the positive integers such that 4k2n + 1 = da2, k > 1, n > 2and d is square free. Further let C(K) and h(K) denote the ideal class group andclass number of the real quadratic field K = Q(W). In this paper, we prove that ifa < 0.5ho,56n, then h(K) = 0 (mod n) and C(K) has a cyclic subgroup with order n. |
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| Keywords: | Real quadratic field Ideal class group Cyclic subgroup Class number Divisibility |
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