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