List questions from galois-extensions

Published on 29 Dec 2019 - 15:51

201

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Construct Galois field extension from a given a Galois Field

Published on 29 Dec 2019 - 18:05

202

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

Published on 02 Jan 2020 - 6:25

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

71

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

Published on 08 Jan 2020 - 15:15

75

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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 08 Jan 2020 - 17:49

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

137

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Proof of Galois criterion

Published on 17 Jan 2020 - 8:54

132

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

Published on 25 Mar 2026 - 6:28

32

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

Published on 25 Mar 2026 - 4:39

88

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exhib power of alpha of GF(256)

Published on 19 Jan 2020 - 15:51

241

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

Published on 25 Mar 2026 - 6:29

57

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Find the lattice of intermediate subgroups of a Galois group.

Published on 28 Jan 2020 - 15:00

63

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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 29 Jan 2020 - 11:01

552

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

Published on 31 Jan 2020 - 18:20

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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