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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

[ 1 ] Artin, E. and Tate, J., Class field theory, Benjamin, W. A., Inc., New York · Amsterdam, 1967.Google Scholar
[ 2 ] Huppert, B., Endliche Gruppen I, Springer-Verlag, Berlin · Heidelberg·New York, 1967.Google Scholar
[ 3 ] Miyake, K., On the structure of the idele group of an algebraic number field, Nagoya Math. J., 80 (1980), 117–127.Google Scholar
[ 4 ] Miyake, K., On the units of an algebraic number field, J. Math. Soc. Japan, 34 (1982), 515–525.CrossRefGoogle Scholar
[ 5 ] Miyake, K., Central extensions and Schur’s multiplicators of Galois groups, Nagoya Math. J., 90 (1983), 137–144.Google Scholar
[ 6 ] Opolka, H., Zur Auflösung zahlentheoretischer Knoten, Math. Z., 173 (1980), 95–103.Google Scholar
[ 7 ] Opolka, H., Some remarks on the Hasse norm theorem, Proc. Amer. Math. Soc, 84 (1982), 464–466.Google Scholar
[ 8 ] Shirai, S., On the central class field mod m of Galois extensions of an algebraic number field, Nagoya Math. J., 71 (1978), 61–85.CrossRefGoogle Scholar