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On central extensions of a Galois extension of algebraic number fields

Published online by Cambridge University Press:  22 January 2016

Katsuya Miyake
Katsuya Miyake*
Affiliation:
Department of Mathematics, College of General Education Nagoya University, Chikusa-ku, Nagoya 464, Japan
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Let k be an algebraic number field of finite degree, and K a finite Galois extension of k. A central extension L of K/k is an algebraic number field which contains K and is normal over k, and whose Galois group over K is contained in the center of the Galois group Gal(L/k). We denote the maximal abelian extensions of k and K in the algebraic closure of k by kab and Kab respectively, and the maximal central extension of K/k by MCK/k. Then we have Kab⊃MCK/k⊃kab·K.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 93 , March 1984 , pp. 133 - 148
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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