# Non-Abelian number field

From Encyclopedia of Mathematics

An algebraic number field with a non-Abelian Galois group over the field of rational numbers $ \mathbf Q $,
or a field that is not normal over $ \mathbf Q $.
Sometimes, instead of $ \mathbf Q $,
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 $.

#### Comments

#### 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=47981

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