Vol. 63, No. 2, 1976

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Genera in normal extensions

Robert Gold

Vol. 63 (1976), No. 2, 397–400

Let K∕F be a finite normal extension of algebraic number fields and let CK be the ideal class group of K. There are two fundamentally different ways to define the principal genus of CK with respect to F. Classically the principal genus is described by norm residue symbols. By the modern definition it is the class group of the maximal unramified extension of K which is the composite of K with an abelian extension of F. It is shown here that the two definitions are equivalent.

Mathematical Subject Classification
Primary: 12A65, 12A65
Secondary: 12A40
Received: 17 July 1975
Published: 1 April 1976
Robert Gold