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ON UNRAMIFIED SOLVABLE EXTENSIONS OF SMALL NUMBER FIELDS
Published online by Cambridge University Press: 09 November 2020
Abstract
We investigate unramified extensions of number fields with prescribed solvable Galois group G and certain extra conditions. In particular, we are interested in the minimal degree of a number field K, Galois over $\mathbb {Q}$ , such that K possesses an unramified G-extension. We improve the best known bounds for the degree of such number fields K for certain classes of solvable groups, in particular for nilpotent groups.
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- © 2020 Australian Mathematical Publishing Association Inc.