New posts in Galois Theory

$\mathbb{Q}(\sqrt{p+\sqrt{p}})$ is Galois over $\mathbb{Q} \iff p=n^2+1$ for a prime $p$.

Is $\sqrt{3-\sqrt{3}} \in L = \mathbb{Q}(\sqrt{3+\sqrt{3}})$?

Aesthetic proofs that involve Field Theory / Galois Theory

Is the composite of two simple radical extensions another simple radical extension?

Find an example about splitting field

If every polynomial in $k[x]$ has a root in $E$, is $E$ algebraically closed?

Quartic as a product of quadratics

Does this Galois group determine the class ideal class group?

Computing $\phi(\frac32)$ where $\phi$ is an automorphism of $\mathbb Q[\sqrt2]$ such that $\phi(1)=1$ and $\phi(\sqrt2)=\sqrt2$

Prove that $[\mathbf{Q}(\sqrt{1+i},\sqrt{2}):\mathbf{Q}]=8$.