New posts in galois-theory

Why these 'elementary' facts do not solve the Inverse Galois Problem?

abstract-algebra group-theory galois-theory

Galois group of $x^{8}+16$

A question regarding the definition of Galois group

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

Learning about Grothendieck's Galois Theory.

algebraic-geometry reference-request category-theory galois-theory book-recommendation

When is a Morphism between Curves a Galois Extension of Function Fields

algebraic-geometry field-theory galois-theory algebraic-curves

Galois action on a uniformizer of a non-archimedean local field

galois-theory p-adic-number-theory local-field

So-called Artin-Schreier Extension

galois-theory extension-field

Let $a$ be a p-cycle in $S_p$, and let $b$ be a transposition in $S_p$. Show $S_p$ is generated by $a$ and $b$.

abstract-algebra group-theory permutations galois-theory symmetric-groups

Galois closure of a $p$-extension is also a $p$-extension

group-theory field-theory galois-theory

Symmetric functions written in terms of the elementary symmetric polynomials.

combinatorics galois-theory symmetric-polynomials elementary-functions symmetric-functions

$X^m-a$ and $X^m-b$ irreducible with same splitting field, prove relation between $a$ and $b$.

Grothendieck's Galois theory: fundamental theorem

category-theory galois-theory group-actions

Prove $j:D\to \text{Hom}_R(S,S)$ is left $S$-module homomorphism

abstract-algebra ring-theory modules galois-theory group-homomorphism

Finding the degree of a field extension over the rationals

field-theory galois-theory

Is the size of the Galois group always $n$ factorial?

abstract-algebra field-theory galois-theory

$K(u,v)$ is a simple extension of fields if $u$ is separable

field-theory galois-theory extension-field

Radical extension

abstract-algebra field-theory galois-theory roots-of-unity

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

abstract-algebra group-theory polynomials galois-theory solvable-groups

Is $x+x^{2^t}$ a cube in the finite fields with characteristic 2?

abstract-algebra galois-theory finite-fields elliptic-curves

Complex Galois Representations are Finite

number-theory representation-theory galois-theory