Is there a necessary and sufficient condition for when a cubic extension of $\mathbb{Q}$ is not a Galois extension?
Non-Galois cubic extensions
4
$\begingroup$
abstract-algebra
galois-theory
-
0It is sufficient that the extension is with a real root of $x^3 - m$, with $m \neq 0,1$ without cube factors. (Since the extension is not normal in this case). OK, I now see you wanted "iff" conditions, I didn't notice that until now. Sorry, I'll leave this comment anyway... – 2012-07-07