New posts in galois-theory

Every finite abelian group is the Galois group of some finite extension of the rationals

group-theory galois-theory

Galois group of the splitting field of the polynomial $x^5 - 2$ over $\mathbb Q$

abstract-algebra number-theory field-theory galois-theory frobenius-groups

Galois group of $X^4 + 4X^2 + 2$ over $\mathbb Q$.

abstract-algebra galois-theory

Constructive Proof of Kronecker-Weber?

abstract-algebra galois-theory constructive-mathematics

When the group of automorphisms of an extension of fields acts transitively

field-theory galois-theory

Tower of Galois Extensions [duplicate]

galois-theory

Existence of Polynomial with whom product contains only prime powers

abstract-algebra polynomials galois-theory

$x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$

field-theory galois-theory irreducible-polynomials

why are subextensions of Galois extensions also Galois?

field-theory galois-theory

How do I solve the quintic $n^5-m^4n+\frac{P}{2m}=0$ for $n$?

abstract-algebra trigonometry galois-theory solvable-groups quintics

Find all the intermediate fields of the splitting field of $x^4 - 2$ over $\mathbb{Q}$

abstract-algebra field-theory galois-theory splitting-field

A characterisation of quadratic extensions contained in cyclic extensions of degree 4

galois-theory

Splitting field of $x^{n}-1$ over $\mathbb{Q}$

abstract-algebra field-theory galois-theory

Determining the Galois group of a cubic without using discriminant

abstract-algebra group-theory field-theory galois-theory

Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$

field-theory galois-theory

Finding the intermediate fields of $\Bbb{Q}(\zeta_7)$.

abstract-algebra galois-theory

Showing field extension $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})/\mathbb{Q}$ degree 8 [duplicate]

abstract-algebra galois-theory field-theory

Confusion concerning Lemma 1.12 in Wiles's proof of Fermat's Last Theorem

linear-algebra proof-explanation representation-theory galois-theory galois-representations

Show that $x^n + x + 3$ is irreducible for all $n \geq 2.$

polynomials galois-theory irreducible-polynomials

Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?

abstract-algebra field-theory galois-theory extension-field