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Galois Group of the Maximal Abelian Extension over an Algebraic Number Field

Published online by Cambridge University Press:  22 January 2016

Tomio Kubota
Tomio Kubota*
Affiliation:
Mathematical Institute, Nagoya University
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The aim of the present work is to determine the Galois group of the maximal abelian extension ΩA over an algebraic number field Ω of finite degree, which we fix once for all.

Let Z be a continuous character of the Galois group of ΩA/Ω. Then, by class field theory, the character Z is also regarded as a character of the idele group of Ω. We call such Z character of Ω. For our purpose, it suffices to determine the group Xl of the characters of Ω whose orders are powers of a prime number l.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 177 - 189
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

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