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A Property of Meta-Abelian Extensions

Published online by Cambridge University Press:  22 January 2016

Yoshiomi Furuta
Yoshiomi Furuta*
Affiliation:
Mathematical Institute, Nagoya University
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Let k be an algebraic number field of finite degree, A the maximal abelian extension over k, and M a meta-abelian field over h of finite degree, that is, M/k be a normal extension over k of finite degree with an abelian group as commutator group of its Galois group.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 19 , October 1961 , pp. 169 - 187
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1961

References

[1] Fröhlich, A., A prime decomposition symbol for certain non Abelian number fields, Acta Sci. Math., 21 (1960), pp. 229–246.Google Scholar
[2] Furuta, Y., On meta-abelian fields of a certain type, Nagoya Math. J., 14 (1959), pp. 193–199.CrossRefGoogle Scholar
[3] Hasse, H., Zum Existenzsatz von Grunwald in der Klassenkörpertheorie, J. Reine Angew. Math., 188 (1950), pp. 40–64.CrossRefGoogle Scholar