New posts in Galois Theory

The Automorphism Group $\Gamma(\mathbb{Q}(\sqrt[n]{2}):\mathbb{Q})$ is trivial if $n$ is odd.

If $n>1$, are there $f_1,\dots,f_k\in\mathbb{Z}[x]$ of degree $n$ such that, for any prime $p$, some $f_i$ is irreducible and of degree $n$, mod $p$?

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.

Galois group of a degree 6 polynomial

Correct my intuition: every Galois group is $S_n$, and other obviously incorrect statements

Galois Group of $x^4 - 7$ over $\mathbb{F}_5$

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