Must a degree $6$ field extension with Galois group $S_3$ be the splitting field of a cubic?
129687
Does a Galois group being $S_3$ correspond to the extension being the splitting field of a cubic?
114295
Find all the middle fields of the splitting field of $x^4-2$ over $\mathbb{Q}$
8602
Galois Group of $(x^2-p_1)\cdots(x^2-p_n)$
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
122952
Degree of extension is equal to linear combination of prime factor multiplicities with prime factor index coefficients in Dedekind domains
46648
How to prove the existence of a splitting field?
126127
A field extension of prime degree
19525
Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8
104634
Galois extension is (not) transitive
12524
Galois group of $x^3 - 2 $ over $\mathbb Q$
94382
Calculate the degree of the extension $[\mathbb{Q}(\cos(\frac{2\pi}{p})):\mathbb{Q}]$
3161
Galois group of $x^6 + 3$ isomorphic to a copy of $S_3$ inside $S_6$
56420
Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$
116628
Example of Galois extension whose Galois group is $A_4$
158588
Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
108914
Splitting field of $x^n-a$ contains all $n$ roots of unity