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On a method for the determination of class number factors in number fields

Published online by Cambridge University Press:  26 February 2010

A. Fröhlich
A. Fröhlich
Affiliation:
King's College, London.
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Extract

In the present paper a simple technique will be developed for the arithmetical determination of certain class group components and class number factors in finite number fields. This technique is based on classical theories (Hilbert's work on inertia groups, the theory of absolutely Abelian fields as class fields of congruence groups, absolute class fields of number fields). In keeping with the traditional approach to the subject we shall use here the language of ideal theory. The only non-classical concepts to be used (which, however, are of fundamental importance) are those of the inertia groups and the congruence groups associated to p-adic fields. We shall also give some illustrations of the use of our technique in some special cases. Further applications will follow in subsequent papers.

Type
Research Article
Information
Mathematika , Volume 4 , Issue 2 , December 1957 , pp. 113 - 121
Copyright
Copyright © University College London 1957

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References

1.Fröhlich, A., “On the absolute class group of Abelian fields”, J. London Math. Soc, 29 (1954), 211–217.CrossRefGoogle Scholar
2.Furtwängler, Ph., “Über die Klassenzahlen der Kreisteilungskörper”, J. für die reine u. angew. Math., 140 (1911), 29–32.CrossRefGoogle Scholar
3.Hecke, E., Vorlesungen über die Theorie der algebraischen Zahlen (Reprinted by Chelsea Press, New York, 1948).Google Scholar