Non-Abelian number field

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An algebraic number field with a non-Abelian Galois group over the field of rational numbers $\QQ$, or a field that is not normal over $ \QQ$. Sometimes, instead of $\QQ$, one considers some other ground field $k$ of algebraic numbers, and the term "non-Abelian" is understood to refer to the Galois group over $k$.


[a1] E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9
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Non-Abelian number field. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.V. Kuz'min (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article