New posts in Galois Theory

"Golden Ratio" for $n$ subsegments

When does a permutation of the roots define an automorphism?

Let $F$ be a field of characteristic not $2$, and let $K$ be an extension of $F$ with $[K: F] = 2$. Show that $K = F (\sqrt{a})$ for some $a\in F$

Are there $x,y,z \in \mathbb Q \left(\sqrt[3]{2} \exp\left(\frac{2\pi i}{3}\right)\right)$ such that $x^2+y^2+z^2=-1$?

About primes and cyclotomic extensions

Galois group of an irreducible , separable polynomial be abelian , then each of the roots of the polynomial generates the splitting field?

Why does "solvability" for groups suggest something about the solution of polynomials?

Galois theory and cryptography

How can I show that the polynomial $p = x^5 - x^3 - 2x^2 - 2x - 1$ is irreducible over $\Bbb Q$?

Real Cyclic Extensions of $\mathbb Q$ of given degree