Infinite Family of Imaginary Cyclic Fields of Degree p-1 with the p-Rank of the Ideal Class Groups of at Least Two

作     者：Shin-ichi Katayama Yasuhiro Kishi 

作者机构：Department of Mathematical Sciences Tokushima University 1-1 Minamijosanjima-cho Tokushima-shi Tokushima 770-8502 Japan Department of Mathematics Fukuoka University of Education 1-1 Bunkyoumachi Akama Munakata-shi Fukuoka 811-4192 Japan 

出 版 物：《Tsinghua Science and Technology》 (清华大学学报（自然科学版（英文版）)

年 卷 期：2007年第12卷第4期

页      面：475-478页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by the Japan Society for the Promotion of Science (JSPS) (No. 14540030) the JSPS Research Fellowships for Young Scientists 

主　　题：ideal class group imaginary cyclic field Lucas sequence 

摘      要：Imaginary cyclic fields of degree p-1 which have two distinct unramified cyclic extensions of degree p are produced using elementary properties of the Lucas sequences. An infinite family of imaginary cyclic fields of degree p-1 are then given with the p-rank of the ideal class groups of at least two.