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I am revising Galois Theory and am faced with the following problem. Let $L/K$ be a finite Galois extension whose Galois group is isomorphic to $S_n$. Show that L is the splitting field of a separable polynomial of degree $n$. My idea, is that since the extension is normal, we know $L = $ Split$_K(f)$ for some $f\in K[X]$, so we want to use Orbit-Stabilizer or something to show $deg(f) = n$.

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  • $\begingroup$ "Revising" or "Revisiting"? ;-) $\endgroup$ – Adrian Keister Apr 26 '18 at 14:41
  • $\begingroup$ Sorry? I Haven't seen this problem before. $\endgroup$ – Elie Bergman Apr 26 '18 at 14:45
  • $\begingroup$ If you are "revising" Galois Theory, you are changing the theory, which, considering how well-established it is, I wouldn't advise you do. If you are "revisiting" Galois Theory, then you are re-learning it, which is a great thing to do. $\endgroup$ – Adrian Keister Apr 26 '18 at 14:48
  • $\begingroup$ Related: math.stackexchange.com/questions/2292604/… $\endgroup$ – Eric Towers Apr 26 '18 at 14:48

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