List questions from galois-theory

Published on 20 Apr 2018 - 15:56

389

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How to show that the two extensions are isomorphic?

Published on 25 Mar 2026 - 15:49

90

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Galois field over $\mathbb{Z}_{2}$.

Published on 26 Mar 2026 - 1:26

201

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If $E= \mathbb{Q}(\sqrt{2} + \sqrt{7})$ Show that $E/\mathbb{Q}$ is a Galois Extension.

Published on 25 Mar 2026 - 9:48

153

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Find all integers n such that its root is in Q adjoin root 2

Published on 25 Mar 2026 - 15:51

176

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irreducible polynomial over finite field.

Published on 25 Mar 2026 - 17:50

293

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Question about Galois Extension and fixed field by a Subgroup of the Galois group

Published on 25 Mar 2026 - 15:53

152

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Determine invariant subfield and order in $\operatorname{Aut}(L)$

Published on 25 Mar 2026 - 9:27

402

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Prove that there is a Galois extension $E$ of $\mathbb{Q}$ such that Gal$(E/\mathbb{Q}) \cong \mathbb{Z}_{18}$

Published on 27 Mar 2026 - 3:43

250

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What is Gal$_\mathbb{Q}(x^4 + 5x^3 + 10x + 5)$?

Published on 22 Mar 2026 - 19:40

241

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For any field $K$, $t^3+xt+1$ is either irreducible or splits in $K$

Published on 24 Apr 2018 - 6:18

53

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Let $θ$ have minimal polynomial $t^3 +at^2 +bt +c$ over $\mathbb{Q}$. In what conditions in terms of $a,b,c$ $θ =φ^2$ where $φ ∈\mathbb{Q}(θ)$

Published on 24 Apr 2018 - 6:41

484

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Find all the conjugates of primitive $35th$ root of unity over $\mathbb{F_{13}}$

Published on 26 Mar 2026 - 1:29

280

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Show the Galois group of $f(x)=x^p - 2$ is isomorphic to $\mathbb{Z}_p$

Published on 25 Mar 2026 - 14:25

86

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Proving a Galois group is not contained in $A_4$

Published on 25 Mar 2026 - 10:55

List Question

Reference Request: Abstract Exposition of Galois Theory

How to show that the two extensions are isomorphic?

Galois field over $\mathbb{Z}_{2}$.

If $E= \mathbb{Q}(\sqrt{2} + \sqrt{7})$ Show that $E/\mathbb{Q}$ is a Galois Extension.

Find all integers n such that its root is in Q adjoin root 2

irreducible polynomial over finite field.

Question about Galois Extension and fixed field by a Subgroup of the Galois group

Determine invariant subfield and order in $\operatorname{Aut}(L)$

Prove that there is a Galois extension $E$ of $\mathbb{Q}$ such that Gal$(E/\mathbb{Q}) \cong \mathbb{Z}_{18}$

What is Gal$_\mathbb{Q}(x^4 + 5x^3 + 10x + 5)$?

For any field $K$, $t^3+xt+1$ is either irreducible or splits in $K$

Let $θ$ have minimal polynomial $t^3 +at^2 +bt +c$ over $\mathbb{Q}$. In what conditions in terms of $a,b,c$ $θ =φ^2$ where $φ ∈\mathbb{Q}(θ)$

Find all the conjugates of primitive $35th$ root of unity over $\mathbb{F_{13}}$

Show the Galois group of $f(x)=x^p - 2$ is isomorphic to $\mathbb{Z}_p$

Proving a Galois group is not contained in $A_4$

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