Question

Find the Galois group $Gal(\mathbb{Q}[\sqrt{2}]/\mathbb{Q})$ and determine all intermediate subfields explicitly.

score 106 · Answer 1 · 2026-03-28 14:37:49

106

Views

Find the Galois group $Gal(\mathbb{Q}[\sqrt{2}]/\mathbb{Q})$ and determine all intermediate subfields explicitly.

Published on 28 Mar 2026 - 14:37

score 52 · Answer 2 · 2026-03-26 16:14:43

52

Views

Number of primitive elements for $\mathbb{F}_{p^{n}}$ over $\mathbb{F}_{p^{m}}$ if $1\neq m\mid n$.

Published on 26 Mar 2026 - 16:14

score 120 · Answer 3 · 2026-03-28 14:37:56

120

Views

Find $\mathrm{Gal}(\mathbb{Q}[\sqrt{13}, \sqrt{17}]/\mathbb{Q})$ and explicitly determine the intermediate subfields

Published on 28 Mar 2026 - 14:37

score 252 · Answer 4 · 2026-03-28 14:37:08

252

Views

Seeking counterexample to the modulo $p$ reduction method in finding Galois group.

Published on 28 Mar 2026 - 14:37

score 484 · Answer 5 · 2026-03-26 16:11:29

484

Views

Constructive Inverse Galois Problem for finite abelian groups

Published on 26 Mar 2026 - 16:11

score 43 · Answer 6 · 2026-03-28 14:44:23

43

Views

Galois Extension and Principal ideal in $F[x]$

Published on 28 Mar 2026 - 14:44

score 37 · Answer 7 · 2026-04-12 03:11:08

37

Views

Action of Galois group and direct product

Published on 12 Apr 2026 - 3:11

score 401 · Answer 8 · 2026-03-28 14:44:25

401

Views

Computing the Galois group of the extension $\mathbb{C}(x,y)/\mathbb{C}(x^a y^b, x^c y^d)$

Published on 28 Mar 2026 - 14:44

score 632 · Answer 9 · 2026-03-28 14:44:11

632

Views

Calculation of the fixed field of a subgroup of a Galois group

Published on 28 Mar 2026 - 14:44

score 196 · Answer 10 · 2026-03-26 16:14:12

196

Views

Finding primitive element of field extension in characteristic 2 corresponding under Galois correspondence to the group $G_f\cap A_n$

Published on 26 Mar 2026 - 16:14

score 74 · Answer 11 · 2026-03-28 14:44:23

74

Views

Show $\mathbb Q(u,i)\neq\mathbb Q(u)$ where $u$ is a root of $t^4-3t^2+4$

Published on 28 Mar 2026 - 14:44

score 1.5k · Answer 12 · 2026-03-28 14:44:25

1.5k

Views

Galois group of $x^5-x-1$ over $\Bbb Q$

Published on 28 Mar 2026 - 14:44

score 95 · Answer 13 · 2026-03-28 14:37:16

95

Views

Intersection in infinite Galois theory

Published on 28 Mar 2026 - 14:37

score 62 · Answer 14 · 2026-03-28 14:37:16

62

Views

Question about biquadratic extension over $\mathbb{Q}$

Published on 28 Mar 2026 - 14:37

score 180 · Answer 15 · 2026-03-28 14:36:57

180

Views

Understanding/computing quadratic Gauss Sum

Published on 28 Mar 2026 - 14:36

List Question

Find the Galois group $Gal(\mathbb{Q}[\sqrt{2}]/\mathbb{Q})$ and determine all intermediate subfields explicitly.

Number of primitive elements for $\mathbb{F}_{p^{n}}$ over $\mathbb{F}_{p^{m}}$ if $1\neq m\mid n$.

Find $\mathrm{Gal}(\mathbb{Q}[\sqrt{13}, \sqrt{17}]/\mathbb{Q})$ and explicitly determine the intermediate subfields

Seeking counterexample to the modulo $p$ reduction method in finding Galois group.

Constructive Inverse Galois Problem for finite abelian groups

Galois Extension and Principal ideal in $F[x]$

Action of Galois group and direct product

Computing the Galois group of the extension $\mathbb{C}(x,y)/\mathbb{C}(x^a y^b, x^c y^d)$

Calculation of the fixed field of a subgroup of a Galois group

Finding primitive element of field extension in characteristic 2 corresponding under Galois correspondence to the group $G_f\cap A_n$

Show $\mathbb Q(u,i)\neq\mathbb Q(u)$ where $u$ is a root of $t^4-3t^2+4$

Galois group of $x^5-x-1$ over $\Bbb Q$

Intersection in infinite Galois theory

Question about biquadratic extension over $\mathbb{Q}$

Understanding/computing quadratic Gauss Sum

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