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

Shin-ichi Katayama, Yasuhiro Kishi†( )
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
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Abstract

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.

Keywords

ideal class groupimaginary cyclic fieldLucas sequence

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Tsinghua Science and Technology
Volume 12 Issue 4,
August 2007
Pages 475-478
DOI: 10.1016/S1007-0214(07)70070-6

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Katayama S-i, Kishi Y. Infinite Family of Imaginary Cyclic Fields of Degree p-1 with the p-Rank of the Ideal Class Groups of at Least Two. Tsinghua Science and Technology, 2007, 12(4): 475-478. https://doi.org/10.1016/S1007-0214(07)70070-6

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Received: 13 February 2006
Published: 01 August 2007
© Tsinghua University Press 2007