List questions from galois-extensions

Published on 15 Apr 2026 - 21:21

203

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cardinality of Galois group in $\mathbb{Q}$($\zeta_n$)

Published on 11 May 2026 - 9:07

817

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Compute the degree of the splitting field of $x^{12} - 2$ over $\mathbb{Q}$ and describe its Galois Group as a semidirect product

Published on 11 May 2026 - 3:49

124

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Primes lying above a prime in a Galois extension

Published on 14 Apr 2026 - 18:55

62

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Question regarding Galois theory

Published on 14 Apr 2026 - 6:48

598

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Galois group is determined by action on roots of polynomial

Published on 12 Apr 2026 - 19:37

197

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Is this a counterexample?

Published on 10 Apr 2026 - 15:37

160

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Any Sub-extension of a Radical Extension is Solvable?

Published on 15 Apr 2026 - 3:54

71

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Can we have two different polynomials of the same degree $d$ here in the factorisation of $x^{p^n} -x$?

Published on 15 Apr 2026 - 0:38

191

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Determine a Normal Basis for Galois Extension of $\mathbb{Q}$ with primitive pth root of unit (p prime)

Published on 10 May 2026 - 20:03

332

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Prove that $[\mathbb{Q}(\sqrt{4+\sqrt{5}},\sqrt{4-\sqrt{5}}):\mathbb{Q}] = 8$.

Published on 11 May 2026 - 8:32

161

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Degree of extension - Is this $\phi(n)$ or $\phi(n)/2$?

Published on 17 Apr 2026 - 13:41

401

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cyclic extension of prime power of a local field

Published on 10 May 2026 - 17:38

894

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Normal Subgroup of Galois Group

Published on 14 Apr 2026 - 8:16

164

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Splitting field of an irreductible polynomial $f(X) \in F_{q}[X]$

Published on 11 May 2026 - 5:07

List Question

Galois group of $x^3+x+1$ over $\mathbb{Q}$ is isomorphic to $S_3 $

cardinality of Galois group in $\mathbb{Q}$($\zeta_n$)

Compute the degree of the splitting field of $x^{12} - 2$ over $\mathbb{Q}$ and describe its Galois Group as a semidirect product

Primes lying above a prime in a Galois extension

Question regarding Galois theory

Galois group is determined by action on roots of polynomial

Is this a counterexample?

Any Sub-extension of a Radical Extension is Solvable?

Can we have two different polynomials of the same degree $d$ here in the factorisation of $x^{p^n} -x$?

Determine a Normal Basis for Galois Extension of $\mathbb{Q}$ with primitive pth root of unit (p prime)

Prove that $[\mathbb{Q}(\sqrt{4+\sqrt{5}},\sqrt{4-\sqrt{5}}):\mathbb{Q}] = 8$.

Degree of extension - Is this $\phi(n)$ or $\phi(n)/2$?

cyclic extension of prime power of a local field

Normal Subgroup of Galois Group

Splitting field of an irreductible polynomial $f(X) \in F_{q}[X]$

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