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April 2016 On some properties of Galois groups of unramified extensions
Mamoru Asada
Osaka J. Math. 53(2): 321-330 (April 2016).

Abstract

Let $k$ be an algebraic number field of finite degree and $k_{\infty}$ be the maximal cyclotomic extension of $k$. Let $\tilde{L}_{k}$ and $L_{k}$ be the maximal unramified Galois extension and the maximal unramified abelian extension of $k_{\infty}$ respectively. We shall give some remarks on the Galois groups $\mathrm{Gal}(\tilde{L}_{k}/k_{\infty})$, $\mathrm{Gal}(L_{k}/k_{\infty})$ and $\mathrm{Gal}(\tilde{L}_{k}/k)$. One of the remarks is concerned with non-solvable quotients of $\mathrm{Gal}(\tilde{L}_{k}/k_{\infty})$ when $k$ is the rationals, which strengthens our previous result.

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Mamoru Asada. "On some properties of Galois groups of unramified extensions." Osaka J. Math. 53 (2) 321 - 330, April 2016.

Information

Published: April 2016
First available in Project Euclid: 27 April 2016

zbMATH: 1350.11096
MathSciNet: MR3492801

Subjects:
Primary: 11R18 , 11R23

Rights: Copyright © 2016 Osaka University and Osaka City University, Departments of Mathematics

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Vol.53 • No. 2 • April 2016
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