On the Exponent of the Ideal Class Groups of Complex Quadratic Fields

Proceedings of the American Mathematical Society ◽

10.2307/2037547 ◽

1972 ◽

Vol 31 (2) ◽

pp. 433 ◽

Author(s):

David W. Boyd ◽

H. Kisilevsky

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

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On the exponent of the ideal class groups of complex quadratic fields.

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1972-0289454-4 ◽

1972 ◽

Vol 31 (2) ◽

pp. 433-433

Author(s):

David W. Boyd ◽

H. Kisilevsky

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

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On the Stark–Shintani units and the ideal class groups in the cyclotomic Zp-extensions of class fields over real quadratic fields

Acta Arithmetica ◽

10.4064/aa102-1-2 ◽

2002 ◽

Vol 102 (1) ◽

pp. 21-26 ◽

Author(s):

Tsuyoshi Itoh

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Real Quadratic Fields ◽

Ideal Class Groups ◽

Class Fields ◽

Real Quadratic ◽

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The selmer groups of elliptic curves and the ideal class groups of quadratic fields

Communications in Algebra ◽

10.1080/00927879708825980 ◽

1997 ◽

Vol 25 (7) ◽

pp. 2157-2167

Author(s):

Yen-Mei J. Chen

Keyword(s):

Elliptic Curves ◽

Quadratic Fields ◽

Selmer Groups ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

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The ideal class groups of dihedral extensions over imaginary quadratic fields and the special values of the Artin L-function

Journal of Number Theory ◽

10.1016/j.jnt.2010.11.011 ◽

2011 ◽

Vol 131 (6) ◽

pp. 1062-1069

Author(s):

Yutaka Konomi

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Special Values ◽

Ideal Class Groups ◽

Dihedral Extensions ◽

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A criterion for a certain type of imaginary quadratic fields to have $3$-ranks of the ideal class groups greater than one

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.74.93 ◽

1998 ◽

Vol 74 (6) ◽

pp. 93-97 ◽

Author(s):

Yasuhiro Kishi

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Ideal Class Groups ◽

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Norms from quadratic fields and their relation to noncommuting 2�2 matrices III. A link between the 4-rank of the ideal class groups inQ $$(\sqrt m )$$ and inQ $$(\sqrt { - m} )$$

Mathematische Zeitschrift ◽

10.1007/bf01241822 ◽

1977 ◽

Vol 154 (2) ◽

pp. 91-95 ◽

Author(s):

Olga Taussky

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

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On the 2-rank of the ideal class groups of pure number fields

Archiv der Mathematik ◽

10.1007/bf01198128 ◽

1984 ◽

Vol 42 (1) ◽

pp. 53-57

Author(s):

Shin Nakano

Keyword(s):

Number Fields ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

Pure Number ◽

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Imaginary quadratic fields whose ideal class groups have 3-rank at least three

Journal of Number Theory ◽

10.1016/j.jnt.2016.06.019 ◽

2017 ◽

Vol 170 ◽

pp. 46-54

Author(s):

Yasuhiro Kishi ◽

Toru Komatsu

Keyword(s):

Quadratic Fields ◽

Ideal Class ◽

Class Groups ◽

Imaginary Quadratic Fields ◽

Ideal Class Groups

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On the ideal class groups of the maximal real subfields of number fields with all roots of unity

Journal of the European Mathematical Society ◽

10.1007/pl00011159 ◽

1999 ◽

Vol 1 (1) ◽

pp. 35-49 ◽

Author(s):

Masato Kurihara

Keyword(s):

Number Fields ◽

Roots Of Unity ◽

Ideal Class ◽

Class Groups ◽

Ideal Class Groups ◽

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A Note on Ideal Class Groups

Nagoya Mathematical Journal ◽

10.1017/s0027763000012046 ◽

1966 ◽

Vol 27 (1) ◽

pp. 239-247 ◽

Author(s):

Kenkichi Iwasawa

Keyword(s):

Class Group ◽

Cyclotomic Field ◽

Theoretical Method ◽

Number Fields ◽

Ideal Class ◽

Ideal Class Group ◽

Class Groups ◽

Algebraic Number Fields ◽

Ideal Class Groups ◽

In the first part of the present paper, we shall make some simple observations on the ideal class groups of algebraic number fields, following the group-theoretical method of Tschebotarew. The applications on cyclotomic fields (Theorems 5, 6) may be of some interest. In the last section, we shall give a proof to a theorem of Kummer on the ideal class group of a cyclotomic field.

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