Vol. 78, No. 1, 1978

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The 2-class group of biquadratic fields. II

Ezra Brown and Charles John Parry

Vol. 78 (1978), No. 1, 11–26

We describe methods for determining the exact power of 2 dividing the class number of certain cyclic biquadratic number fields. In a recent article, we developed a relative genus theory for cyclic biquadratic fields whose quadratic subfields have odd class number; we considered the case in which the quadratic subfield is Q(√l) with l 5 (mod 8) a prime. Here we shall extend our methods to the cases in which the subfield is Q(√2-) or Q(√l-) with l 1 (mod 8) a prime. We consider all such cases for which the 2-class group of the biquadratic field is of rank at most 3.

Mathematical Subject Classification
Primary: 12A30, 12A30
Received: 23 February 1977
Published: 1 September 1978
Ezra Brown
Charles John Parry