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The 2-Rank of the Class Group of Imaginary Bicyclic Biquadratic Fields

Published online by Cambridge University Press:  20 November 2018

Thomas M. McCall ,
Charles J. Parry  and
Ramona R. Ranalli
Thomas M. McCall
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061-0123
Charles J. Parry
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061-0123
Ramona R. Ranalli
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061-0123
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Abstract

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A formula is obtained for the rank of the 2-Sylow subgroup of the ideal class group of imaginary bicyclic biquadratic fields. This formula involves the number of primes that ramify in the field, the ranks of the 2-Sylow subgroups of the ideal class groups of the quadratic subfields and the rank of a Z2-matrix determined by Legendre symbols involving pairs of ramified primes. As applications, all subfields with both 2- class and class group Z2×Z2 are determined. The final results assume the completeness of D. A. Buell’s list of imaginary fields with small class numbers.

Keywords

11R1611R2911R20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 283 - 300
Copyright
Copyright © Canadian Mathematical Society 1997

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