New posts in Galois Theory

Finding degree of a finite field extension

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

Is the Field Norm of a unit a unit?

How to solve decics like $x^{10}+100x^2+160x+64=0$ having Galois group 10T33?

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

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

Prove that $\sqrt{3\pm\sqrt{7}} \not\in \mathbb{Q}(\sqrt{3\mp\sqrt{7}})$.

How to prove that $(-18+\sqrt{325})^{\frac{1}{3}}+(-18-\sqrt{325})^{\frac{1}{3}} = 3$

Is every primitive element of a finite field of characteristic $2$, a generator of the multiplicative group?

$\mathbb{Q}(\alpha)=\mathbb{Q}(\beta)$ if $\alpha, \beta$ are algebraic over $\mathbb{Q}$ of degree $2$ and $\alpha +\beta$ is a root of a quadratic.