New posts in Galois Extensions

Prove that the Galois group $G = Gal(x^5-2; \mathbb{Q})$ is a group metacyclic.

Let $f(x)= x^3+ax^2+bx+c \in \mathbb{Q}[x]$. Show that the splitting field of $f$ over $\mathbb{Q}$ has degree 1, 2, 3 or 6 over $\mathbb{Q}$.

Showing $K(\sqrt \alpha)/F$ is Galois if and only if $\sigma(\alpha)/\alpha$ is a unit and a square.

Determine the Galois group of $x^3 + 3x^2 - 1$ over $\mathbb{Q}$

For a complex number $\alpha $ which is algebraic over $\Bbb Q$, determining whether $\bar{\alpha}\in \Bbb Q(\alpha)$ or not

Galois group of $x^6-2x^4+2x^2-2$ over $\mathbb{Q}$

Computing the Galois group of the extension $\mathbb{C}(x,y)/\mathbb{C}(x^a y^b, x^c y^d)$

Quadratic subfield of $\mathbb{Q}(\zeta)$

How to calculate the Galois group of $x^5+15x+12$?

Prove that $[\mathbb{Q}(\sqrt{4+\sqrt{5}},\sqrt{4-\sqrt{5}}):\mathbb{Q}] = 8$.