Question

Is it true that $i \in \mathbb{Q}(\sqrt{2},\xi)$, where $\xi = 1_{\frac{2\pi}{3}} = -\frac{1}{2}+i\frac{\sqrt{3}}{2}$?

score 63 · Answer 1 · 2026-04-16 02:47:15

63

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Is it true that $i \in \mathbb{Q}(\sqrt{2},\xi)$, where $\xi = 1_{\frac{2\pi}{3}} = -\frac{1}{2}+i\frac{\sqrt{3}}{2}$?

Published on 16 Apr 2026 - 2:47

score 18 · Answer 2 · 2026-04-13 17:12:47

18

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problem with local Artin map in Hazewinkel article

Published on 13 Apr 2026 - 17:12

score 30 · Answer 3 · 2026-04-14 21:36:00

30

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Primitive element of a finite field whose powers do not lie inside the prime subfield

Published on 14 Apr 2026 - 21:36

score 43 · Answer 4 · 2026-03-25 19:32:49

43

Views

How to calculate Gal$(F(\mu_{p^\infty})/F(\mu_p))$ for a number field $F$?

Published on 25 Mar 2026 - 19:32

score 1.2k · Answer 5 · 2026-04-16 12:29:30

1.2k

Views

Let $F \supset E \supset K$, $E/K$ and $F/E$ Galois and every $\sigma \in \mathrm{Aut}_K(E)$ extendible to $F$. Then $F/K$ is Galois.

Published on 16 Apr 2026 - 12:29

score 267 · Answer 6 · 2026-03-27 13:42:14

267

Views

$L/k$ finite Galois extension with solvable Galois group divisible by a prime $p$ . Does there exist field $k\subseteq F \subseteq L$ s.t. $p=[F:k]$?

Published on 27 Mar 2026 - 13:42

score 110 · Answer 7 · 2026-04-25 12:03:43

110

Views

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score 1.5k · Answer 8 · 2026-03-29 14:02:08

1.5k

Views

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Published on 29 Mar 2026 - 14:02

score 131 · Answer 9 · 2026-03-29 14:07:10

131

Views

Prove an field extension to be Galois

Published on 29 Mar 2026 - 14:07

score 395 · Answer 10 · 2026-03-29 14:03:12

395

Views

Find a field extension given a galois group $Z_{3} \times Z_{3} \times Z_{3}$

Published on 29 Mar 2026 - 14:03

score 362 · Answer 11 · 2026-03-29 14:02:44

362

Views

Find the subfield corresponding to certain subgroup of Galois group

Published on 29 Mar 2026 - 14:02

score 92 · Answer 12 · 2026-03-29 14:06:44

92

Views

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Published on 29 Mar 2026 - 14:06

score 64 · Answer 13 · 2026-03-29 14:03:11

64

Views

Prove that $M=E(\sqrt{a-b\sqrt{c}})$ is the minimal Galois extension of $F$ .

Published on 29 Mar 2026 - 14:03

score 232 · Answer 14 · 2026-03-26 18:49:54

232

Views

Injective K-Homomorphisms are K-Automorphisms

Published on 26 Mar 2026 - 18:49

score 666 · Answer 15 · 2026-03-29 14:02:54

666

Views

Prove that $\mathbb{Q}\left(\sqrt{(2+\sqrt{2})(3+\sqrt{3})}\right)$ is Galois over $\mathbb{Q}$ and determine the Galois group

Published on 29 Mar 2026 - 14:02

List Question

Is it true that $i \in \mathbb{Q}(\sqrt{2},\xi)$, where $\xi = 1_{\frac{2\pi}{3}} = -\frac{1}{2}+i\frac{\sqrt{3}}{2}$?

problem with local Artin map in Hazewinkel article

Primitive element of a finite field whose powers do not lie inside the prime subfield

How to calculate Gal$(F(\mu_{p^\infty})/F(\mu_p))$ for a number field $F$?

Let $F \supset E \supset K$, $E/K$ and $F/E$ Galois and every $\sigma \in \mathrm{Aut}_K(E)$ extendible to $F$. Then $F/K$ is Galois.

$L/k$ finite Galois extension with solvable Galois group divisible by a prime $p$ . Does there exist field $k\subseteq F \subseteq L$ s.t. $p=[F:k]$?

Lattice Extensions

Artin-Schreier Theorem and Galois Extensions

Prove an field extension to be Galois

Find a field extension given a galois group $Z_{3} \times Z_{3} \times Z_{3}$

Find the subfield corresponding to certain subgroup of Galois group

Showing that a quadratic extension of $\mathbb{Q}$ is contained in $\mathbb{R}$

Prove that $M=E(\sqrt{a-b\sqrt{c}})$ is the minimal Galois extension of $F$ .

Injective K-Homomorphisms are K-Automorphisms

Prove that $\mathbb{Q}\left(\sqrt{(2+\sqrt{2})(3+\sqrt{3})}\right)$ is Galois over $\mathbb{Q}$ and determine the Galois group

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