Newbetuts
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New posts in galois-theory
Is there any irreducible polynomial over $\mathbb{Q}$ whose Galois group is $S_4$?
polynomials
galois-theory
Reference request: Abel or Ruffini's proof of the Abel-Ruffini theorem
reference-request
polynomials
galois-theory
Serre's surjective theorem importance.
number-theory
representation-theory
galois-theory
Lines in upper half-space
geometry
galois-theory
hyperbolic-geometry
Field extension of composite degree has a non-trivial sub-extension
field-theory
galois-theory
Absolute Galois Group of $\mathbb{R}(t)$.
abstract-algebra
galois-theory
Separable polynomial definition (Confused)
abstract-algebra
galois-theory
Galois group of $X^5 - X^3 - 2X^2 - 2X - 1$ over $\mathbb{Q}$.
abstract-algebra
galois-theory
A formula for the roots of a solvable polynomial
abstract-algebra
field-theory
galois-theory
When does a formula for the roots of a polynomial exist?
abstract-algebra
polynomials
galois-theory
solvable-groups
Applications of additive version of Hilbert's theorem 90
number-theory
field-theory
algebraic-number-theory
galois-theory
galois-cohomology
Galois over Galois
abstract-algebra
galois-theory
Is the sum of an algebraic and transcendental complex number transcendental?
abstract-algebra
field-theory
galois-theory
transcendental-numbers
What is the condition for a field to make the degree of its algebraic closure over it infinite?
abstract-algebra
field-theory
galois-theory
Are quartic minimal polynomials over $\mathbb{Q}$ always reducible over $\mathbb{F}_p$?
polynomials
galois-theory
finite-fields
Galois group of a degree 5 irreducible polynomial with two complex roots.
group-theory
galois-theory
Why do no prime ideals ramify in the extension $\mathbb{Q}(\sqrt{p }, \sqrt{q})/\mathbb{Q}(\sqrt{pq })$?
abstract-algebra
number-theory
algebraic-number-theory
galois-theory
Finitely Many Extensions of Fixed Degree of a Local Field
abstract-algebra
number-theory
galois-theory
local-field
Suppose $K/F$ is a Galois extension of degree $p^m$. Then there is a chain of extensions $F \subseteq F_1 \subseteq \cdots F_m = K$ each of degree $p$
abstract-algebra
group-theory
field-theory
galois-theory
sylow-theory
Determine the Galois group of the polynomial $(x^3-2)(x^3-3)(x^2-2)$ over $\mathbb{Q}(\sqrt {-3})$
abstract-algebra
field-theory
galois-theory
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