View source for Non-Abelian number field

An algebraic [[Number field|number field]] with a non-Abelian [[Galois group|Galois group]] over the field of rational numbers <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066910/n0669101.png" />, or a field that is not normal over <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066910/n0669102.png" />. Sometimes, instead of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066910/n0669103.png" />, one considers some other ground field <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066910/n0669104.png" /> of algebraic numbers, and the term  "non-Abelian"  is understood to refer to the Galois group over <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066910/n0669105.png" />.



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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E. Weiss,   "Algebraic number theory" , McGraw-Hill  (1963)  pp. Sects. 4–9</TD></TR></table>