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Galois module structure of classgroups and units

Published online by Cambridge University Press:  26 February 2010

M. Taylor
M. Taylor
Affiliation:
Department of Mathematics, King's College, London
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Extract

This paper arises from an attempt to generalise the following result of [1].

THEOREM (Armitage-Fröhlich). If K is a cyclic extension of Q of degree lr, where 2 has even order mod l, then

Type
Research Article
Information
Mathematika , Volume 22 , Issue 2 , December 1975 , pp. 156 - 160
Copyright
Copyright © University College London 1975

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References

1.Armitage, J. V. and Fröhlich, A.. “Classnumber and Unit Signatures”, Mathematika, 14 (1967), 94–98.CrossRefGoogle Scholar
2.Gras, G. and Gras, M. N.. “Signatures des unités cyclotomiques et parité du nombre de classes des extensions cycliques de Q de degré premier impair” (to appear in Annales de l'lnstitut Fourier, Grenoble).Google Scholar
3.Gras, G.. “Signature des unités cyclotomiques et parité du nombre de classes des extensions abeliennes de Q de degré impair” (to appear in Bulletin de la Societe Math, de France).Google Scholar
4.Hecke, E.. Vorlesiwgen iiber die Theorie der algebaischen Zahlen (Chelsea, 1948).Google Scholar
5.Leopoldt, H. W.. “Zur Struktur der l-Klassengruppe galoisscher Zahlkörper”, J. fur reine und ange. Math., 199 (1958).Google Scholar
6.Oriat, B.. “Relation entre les 2-groupes des classes d'idéaux aux sens ordinaire et restreint de certains corps de nombres” (to appear).Google Scholar