# Non-Abelian number field

From Encyclopedia of Mathematics

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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 $k$.

#### References

[a1] | E. Weiss, "Algebraic number theory" , McGraw-Hill (1963) pp. Sects. 4–9 |

**How to Cite This Entry:**

Non-Abelian number field.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Non-Abelian_number_field&oldid=53755

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