New posts in galois-theory

$|\operatorname{Aut}(K/F)| \leq [K:F]_s$ holds in general?

abstract-algebra field-theory galois-theory extension-field automorphism-group

Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?

galois-theory extension-field galois-extensions

Determine the Galois Group of $(x^2-2)(x^2-3)(x^2-5)$

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

The Galois Extension of $\mathbb Q$ with cyclic group of prime order as its Galois group

How to determine the density of the set of completely splitting primes for a finite extension?

algebraic-number-theory galois-theory number-theory

Prove that the tensor product of non algebraic extensions is not a field

abstract-algebra field-theory galois-theory extension-field tensor-products

Normal extension of rational complex fields

abstract-algebra galois-theory

Intermediate fields of cyclotomic splitting fields and the polynomials they split

group-theory galois-theory

Splitting field implies Galois extension

abstract-algebra field-theory galois-theory

How to show $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$?

what is the simplest example of an etale cover which is not Galois?

algebraic-geometry galois-theory

Minimal polynomial of $\zeta+\zeta^{-1}$

abstract-algebra field-theory galois-theory cyclotomic-polynomials

Example of a nontransitive action of $\operatorname{Aut}(K/\mathbb Q)$ on the roots in $K$ of an irreducible polynomial.

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

Source to learn Galois Theory

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Galois group of $x^6+3$ over $\mathbb Q$

abstract-algebra field-theory galois-theory

Intermediate field, normal closure and Galois group

abstract-algebra field-theory galois-theory

Families of Polynomials with specific Galois Group

If a normal $K/F$ has no intermediate extensions, then $[K : F]$ is prime

abstract-algebra field-theory galois-theory

Reading the mind of Prof. John Coates (motive behind his statement)

galois-theory elliptic-curves number-theory algebraic-geometry algebraic-number-theory

Finding a Galois extension of $\Bbb Q$ of degree $3$

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