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• W2910542642 abstract "For various nonsolvable groups $G$, we prove the existence of extensions of the rationals $mathbb{Q}$ with Galois group $G$ and inertia groups of order dividing $ge(G)$, where $ge(G)$ is the smallest exponent of a generating set for $G$. For these groups $G$, this gives the existence of number fields of degree $ge(G)$ with an unramified $G$-extension. The existence of such extensions over $mathbb{Q}$ for all finite groups would imply that, for every finite group $G$, there exists a quadratic number field admitting an unramified $G$-extension, as was recently conjectured. We also provide further evidence for the existence of such extensions for all finite groups, by proving their existence when $mathbb{Q}$ is replaced with a function field $k(t)$ where $k$ is an ample field." @default.
• W2910542642 created "2019-01-25" @default.
• W2910542642 creator A5000793081 @default.
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• W2910542642 date "2019-01-13" @default.
• W2910542642 modified "2023-09-23" @default.
• W2910542642 title "Unramified extensions over low degree number fields" @default.
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• W2910542642 hasPublicationYear "2019" @default.
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