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The genus field and genus group in finite number fields, II

Published online by Cambridge University Press:  26 February 2010

A. Fröhlich
A. Fröhlich
Affiliation:
King's College, London, Strand, W.C.2.
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Extract

In the preceding paper of the same title (cf. [1]) I defined the notion of the principal genus GK of a finite number field K as the least ideal group, which contains the group IK of totally positive principal ideals and is characterized rationally. The quotient group of the group AK of ideals in K modulo GK is the genus group, its order (Ak: GK) = gK is the genus number, which is thus a factor of the class number hK (in the narrow sense). Associated with the genus group is the genus-field, of K, which is defined as the maximal non-ramified extension of K composed of K and of some absolutely Abelian field.

Type
Research Article
Information
Mathematika , Volume 6 , Issue 2 , December 1959 , pp. 142 - 146
Copyright
Copyright © University College London 1959

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References

1.Fröhlich, A., “The genus field and genus group in finite number fields”, Mathematika, 6 (1959), 40–46.Google Scholar
2.Fröhlich, A., “On a method for the determination of class number factors in number fields”, Mathematika, 4 (1957), 113–131.Google Scholar