List questions from galois-theory

Published on 27 Mar 2026 - 17:04

111

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Understanding the Tschirnhaus transformation

Published on 28 Mar 2019 - 10:38

34

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For a finite extension $F$, can we always find a an element a in $F$ s.t $\{a^t\}_{t= 0,...,n-1}$ is a basis of $F$?

Published on 31 Mar 2026 - 6:32

71

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Field Extension equivalence

Published on 28 Mar 2019 - 16:58

409

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Nontrivial Twists of a Vector Bundle

Published on 26 Mar 2026 - 19:09

154

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The solvability group criteria in Cox's Galois Theory

Published on 30 Mar 2019 - 8:14

77

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degree of extension re: roots of unity to the $2^n$ power and their conjugates

Published on 26 Mar 2026 - 14:34

135

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Suppose $a,b\in E$ and $\sigma\in \textrm{Gal}(E/F)$ with $\sigma(a)=b$. Show that $a$ and $b$ have the same minimal polynomial in $F[x]$

Published on 27 Mar 2026 - 23:14

38

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Field extensions contradicting tower law

Published on 31 Mar 2026 - 11:00

143

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Prove that the Galois group is $D_{8}$.

Published on 31 Mar 2019 - 19:39

196

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Galois / Splitting field of $\ \sqrt{\vphantom{\sum}2+{\sqrt2}} $

Published on 25 Mar 2026 - 22:26

122

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$\mathbb{F}_{3}[x]/(x^3-x^2+1) \cong \mathbb{F}_{3}[x]/(x^3-x^2+x+1)$.

Published on 01 Apr 2019 - 1:50

97

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Algebraic Fundamental Group $π_1(U)$

Published on 26 Mar 2026 - 9:37

231

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How to solve decics like $x^{10}+100x^2+160x+64=0$ having Galois group 10T33?

Published on 25 Mar 2026 - 19:09

81

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Precisely which polynomials vanish on $\mathbb{F}_{p^n}$?

Published on 28 Mar 2026 - 14:18

List Question

Galois Group of Q(6th roots of unity) over Q

Understanding the Tschirnhaus transformation

For a finite extension $F$, can we always find a an element a in $F$ s.t $\{a^t\}_{t= 0,...,n-1}$ is a basis of $F$?

Field Extension equivalence

Nontrivial Twists of a Vector Bundle

The solvability group criteria in Cox's Galois Theory

degree of extension re: roots of unity to the $2^n$ power and their conjugates

Suppose $a,b\in E$ and $\sigma\in \textrm{Gal}(E/F)$ with $\sigma(a)=b$. Show that $a$ and $b$ have the same minimal polynomial in $F[x]$

Field extensions contradicting tower law

Prove that the Galois group is $D_{8}$.

Galois / Splitting field of $\ \sqrt{\vphantom{\sum}2+{\sqrt2}} $

$\mathbb{F}_{3}[x]/(x^3-x^2+1) \cong \mathbb{F}_{3}[x]/(x^3-x^2+x+1)$.

Algebraic Fundamental Group $π_1(U)$

How to solve decics like $x^{10}+100x^2+160x+64=0$ having Galois group 10T33?

Precisely which polynomials vanish on $\mathbb{F}_{p^n}$?

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