Question

Is this a valid proof for the normalness of subgroups in galois theory?

score 162 · Answer 1 · 2026-04-13 15:08:54

162

Views

Is this a valid proof for the normalness of subgroups in galois theory?

Published on 13 Apr 2026 - 15:08

score 97 · Answer 2 · 2026-04-17 02:57:53

97

Views

Showing $\mathbb{Q}(\sqrt 2, \sqrt 3 ) = \mathbb{Q}(\sqrt 2 + \sqrt 3)$ using information about Galois group

Published on 17 Apr 2026 - 2:57

score 100 · Answer 3 · 2026-04-14 11:57:42

100

Views

Theorem 17.22 from Ian Stewart's Galois Theory

Published on 14 Apr 2026 - 11:57

score 131 · Answer 4 · 2026-04-14 06:09:24

131

Views

Normal closure as the compositum of conjugates

Published on 14 Apr 2026 - 6:09

score 110 · Answer 5 · 2026-04-16 05:31:11

110

Views

Prove $\operatorname{Gal}(M_3/M_1)\cong\operatorname{Gal}(M_2/(M_1\cap M_2))$

Published on 16 Apr 2026 - 5:31

score 163 · Answer 6 · 2026-04-14 10:33:03

163

Views

How to prove whether $i\in\mathbb{Q}(\cos\frac{2\pi}{5}+i\sin\frac{2\pi}{5})$ or not

Published on 14 Apr 2026 - 10:33

score 177 · Answer 7 · 2026-04-17 11:05:28

177

Views

Find $Gal(\mathbb{Q}(e^{2\pi i/6},e^{2\pi i / 10}) / \mathbb{Q})$

Published on 17 Apr 2026 - 11:05

score 38 · Answer 8 · 2026-04-09 05:55:57

38

Views

How to ensure the generator of Galois extenion?

Published on 09 Apr 2026 - 5:55

score 156 · Answer 9 · 2026-04-11 03:40:35

156

Views

What is $\text{Frob}\in \text{Gal}(\overline{K}/K)$?

Published on 11 Apr 2026 - 3:40

score 199 · Answer 10 · 2026-04-16 04:18:32

199

Views

Showing the extension $\mathbb{Q}(\sqrt[6]{-3})/\mathbb{Q}$ is Galois and determining its Galois group.

Published on 16 Apr 2026 - 4:18

score 294 · Answer 11 · 2026-04-14 14:40:57

294

Views

Is $\mathbb{Q}(\cos\frac{2\pi}{13})/\mathbb{Q}$ a Galois extension?

Published on 14 Apr 2026 - 14:40

score 395 · Answer 12 · 2026-04-13 12:12:36

395

Views

Is the extension of a perfect field by one of its algebraic closures always a Galois extension?

Published on 13 Apr 2026 - 12:12

score 817 · Answer 13 · 2026-04-14 06:45:09

817

Views

Finite Galois group of Galois extension implies that the extension is finite?

Published on 14 Apr 2026 - 6:45

score 245 · Answer 14 · 2026-04-15 23:21:15

245

Views

Adding finite list of square roots of primes to $\mathbb{Q}$

Published on 15 Apr 2026 - 23:21

score 194 · Answer 15 · 2026-04-15 21:19:29

194

Views

$K$ be a finite extension of $\mathbb Q$ then there exists a finite extension $E$ over $K$ such that $E/K$ is not normal.

Published on 15 Apr 2026 - 21:19

List Question

Is this a valid proof for the normalness of subgroups in galois theory?

Showing $\mathbb{Q}(\sqrt 2, \sqrt 3 ) = \mathbb{Q}(\sqrt 2 + \sqrt 3)$ using information about Galois group

Theorem 17.22 from Ian Stewart's Galois Theory

Normal closure as the compositum of conjugates

Prove $\operatorname{Gal}(M_3/M_1)\cong\operatorname{Gal}(M_2/(M_1\cap M_2))$

How to prove whether $i\in\mathbb{Q}(\cos\frac{2\pi}{5}+i\sin\frac{2\pi}{5})$ or not

Find $Gal(\mathbb{Q}(e^{2\pi i/6},e^{2\pi i / 10}) / \mathbb{Q})$

How to ensure the generator of Galois extenion?

What is $\text{Frob}\in \text{Gal}(\overline{K}/K)$?

Showing the extension $\mathbb{Q}(\sqrt[6]{-3})/\mathbb{Q}$ is Galois and determining its Galois group.

Is $\mathbb{Q}(\cos\frac{2\pi}{13})/\mathbb{Q}$ a Galois extension?

Is the extension of a perfect field by one of its algebraic closures always a Galois extension?

Finite Galois group of Galois extension implies that the extension is finite?

Adding finite list of square roots of primes to $\mathbb{Q}$

$K$ be a finite extension of $\mathbb Q$ then there exists a finite extension $E$ over $K$ such that $E/K$ is not normal.

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