List questions from galois-extensions

Published on 28 Mar 2026 - 11:15

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Construct Galois field extension from a given a Galois Field

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203

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Polynomial of degree 5 that has no root in a normal extension, then it is irreducible over that extension

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93

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Existence of elements in $\text{Gal}(\mathbb{Q}(\sqrt[5]{2}, \xi)/\mathbb{Q})$ with $\xi = e^{\frac{2\pi i}{5}}$

Published on 25 Mar 2026 - 20:15

72

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Calculate $[E: \mathbb{Q}]$ and show that $E$ is a Galois extension on $\mathbb{Q}$

Published on 28 Mar 2026 - 11:22

76

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Show that $F$ is a Galois extension on $\mathbb{Z}_p$ and Show that for each $a \in F$ then $a = x^2 + y^2$ with $x,y \in F$

Published on 28 Mar 2026 - 11:21

180

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Number of K-automorphisms of the splitting field of f that switch two roots

Published on 26 Mar 2026 - 14:34

138

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Proof of Galois criterion

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133

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Roots of unity in $\mathcal{O}_{K}$, where $K=\mathbb{Q}(\sqrt{5},\sqrt{-2})$.

Published on 11 May 2026 - 4:17

33

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Is there a solution to speed up the "Galois field" gf function in Matlab

Published on 10 May 2026 - 18:26

89

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exhib power of alpha of GF(256)

Published on 28 Mar 2026 - 11:13

242

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Find all the fixed subfield of $Gal(\mathbb{Q}(\zeta_{40})/\mathbb{Q})$

Published on 11 May 2026 - 9:09

58

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Find the lattice of intermediate subgroups of a Galois group.

Published on 28 Mar 2026 - 11:13

64

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Splitting field's Galois group of $p(X)=X^4+(t^3+1)$ over $\mathbb{Q}(t)$ where $t$ transcendent over $\mathbb{Q}$

Published on 28 Mar 2026 - 11:21

553

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Proof verification -- $x^p - x + a$ is irreducible over a field of characteristic $p$

Published on 28 Mar 2026 - 11:13

List Question

Linearly disjoint number field extensions

Construct Galois field extension from a given a Galois Field

Polynomial of degree 5 that has no root in a normal extension, then it is irreducible over that extension

Existence of elements in $\text{Gal}(\mathbb{Q}(\sqrt[5]{2}, \xi)/\mathbb{Q})$ with $\xi = e^{\frac{2\pi i}{5}}$

Calculate $[E: \mathbb{Q}]$ and show that $E$ is a Galois extension on $\mathbb{Q}$

Show that $F$ is a Galois extension on $\mathbb{Z}_p$ and Show that for each $a \in F$ then $a = x^2 + y^2$ with $x,y \in F$

Number of K-automorphisms of the splitting field of f that switch two roots

Proof of Galois criterion

Roots of unity in $\mathcal{O}_{K}$, where $K=\mathbb{Q}(\sqrt{5},\sqrt{-2})$.

Is there a solution to speed up the "Galois field" gf function in Matlab

exhib power of alpha of GF(256)

Find all the fixed subfield of $Gal(\mathbb{Q}(\zeta_{40})/\mathbb{Q})$

Find the lattice of intermediate subgroups of a Galois group.

Splitting field's Galois group of $p(X)=X^4+(t^3+1)$ over $\mathbb{Q}(t)$ where $t$ transcendent over $\mathbb{Q}$

Proof verification -- $x^p - x + a$ is irreducible over a field of characteristic $p$

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