New posts in galois-theory

Galois group of a degree 6 polynomial

Why $x^{n}=1$'s solution is equal to regular polygon in complex plane?

linear-algebra trigonometry galois-theory

$f$ is irreducible $\iff$ $G$ act transitively on the roots

field-theory galois-theory

Minimal polynomials of $\sin(\pi/8)$ and $\cos(\pi/9)$

galois-theory irreducible-polynomials

How is the degree of the minimal polynomial related to the degree of a field extension?

field-theory galois-theory extension-field

How to compute the Galois group of $x^5+99x-1$ over $\mathbb{Q}$?

abstract-algebra field-theory galois-theory

What is the difference between field theory and Galois theory

soft-question field-theory terminology galois-theory

Number of solns of $x^6+x=a$ in $\mathbb{F}_{2^m}$, where $m\geq 3$ is odd is same as number of solns of $x^2+ax+1=0$

abstract-algebra polynomials field-theory galois-theory finite-fields

$f$ is solvable by radicals, but the splitting field $L:Q$ not radical extension.

field-theory galois-theory

Is there a better way to find the polynomial equation for this curve?

algebraic-geometry galois-theory algebraic-curves

$\bar{\mathbb{F}}_p$ is not a finite degree extension of any proper subfield.

abstract-algebra field-theory galois-theory finite-fields

$\mathbb{Q}(\sqrt{1-\sqrt{2}})$ is Galois over $\mathbb{Q}$

The angle $168^\circ$ is constructible

abstract-algebra field-theory galois-theory contest-math euclidean-geometry

Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible

Galois group of $x^3 + x^2 - 2x - 1$.

abstract-algebra galois-theory

How to prove that if $\sigma\in \operatorname{Gal}(k(x)/k)\Leftrightarrow \sigma(x)=\frac{ax+b}{cx+d}$? [duplicate]

abstract-algebra field-theory galois-theory

Primitive 16th root of unity

Solvable subgroups of $S_p$ of order divisible by $p$

abstract-algebra group-theory galois-theory

$[L:K]=n!\ \Longrightarrow \ f$ is irreducible and $\text{Gal}(L/K)\cong S_n.$

polynomials field-theory galois-theory symmetric-groups irreducible-polynomials

Is $\operatorname{Gal}(\mathbb{Q}_p^{un})\cong \hat{\mathbb{Z}}$?

number-theory algebraic-geometry field-theory galois-theory