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

McCall, Thomas M. ; Parry, Charles J. ; Ranalli, Ramona R.

Canadian journal of mathematics, Tome 49 (1997) no. 2, pp. 283-300

Résumé

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 Z 2×Z 2 are determined. The final results assume the completeness of D. A. Buell’s list of imaginary fields with small class numbers.

Détail

DOI : 10.4153/CJM-1997-014-2

Mots-clés : 11R16, 11R29, 11R20

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