Question

A question on finite normal extension

score 82 · Answer 1 · 2019-04-07 16:44:50

82

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A question on finite normal extension

Published on 07 Apr 2019 - 16:44

score 54 · Answer 2 · 2019-04-07 17:21:27

54

Views

Galois correspondence and invariant fields of L of $f(x)=x^4-2x^2-2$

Published on 07 Apr 2019 - 17:21

score 186 · Answer 3 · 2019-04-07 19:15:02

186

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Let k⊆K⊆E fields and if E/k is a finite extension, the E/K and K/k are also finite extensions.

Published on 07 Apr 2019 - 19:15

score 890 · Answer 4 · 2019-04-07 19:57:32

890

Views

Simple extension and the number of intermediate fields

Published on 07 Apr 2019 - 19:57

score 85 · Answer 5 · 2019-04-07 20:46:13

85

Views

$K$ cannot have subfields $k'$ and $k''$ such $k' \cong \mathbb{Q}$ and $k'' \cong \mathbb{F}_{p}$ where $p$ is some prime.

Published on 07 Apr 2019 - 20:46

score 335 · Answer 6 · 2019-04-07 23:51:52

335

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Galois group of $\mathbb{Q}(\sqrt[5]{3}):\mathbb{Q}$

Published on 07 Apr 2019 - 23:51

score 45 · Answer 7 · 2019-04-08 02:08:26

45

Views

confusion about Galois correspondence

Published on 08 Apr 2019 - 2:08

score 334 · Answer 8 · 2019-04-08 04:33:30

334

Views

Galois group of $\mathbb{Q}(\sqrt[5]{3},\zeta):\mathbb{Q}$

Published on 08 Apr 2019 - 4:33

score 322 · Answer 9 · 2026-03-25 23:13:10

322

Views

Galois group of a quintic with 3 real roots. How to conclude that there's one cycle of order 5?

Published on 25 Mar 2026 - 23:13

score 71 · Answer 10 · 2019-04-08 13:37:56

71

Views

Is there a standard notation for the Galois group of a polynomial?

Published on 08 Apr 2019 - 13:37

score 1k · Answer 11 · 2019-04-08 16:35:23

1k

Views

Find the Galois group of $x^5-6x+3$ over $\mathbb{Q}$

Published on 08 Apr 2019 - 16:35

score 312 · Answer 12 · 2026-03-25 22:30:49

312

Views

Efficiently calculating the Galois group of $p(x)=x^4+4x^2-2$

Published on 25 Mar 2026 - 22:30

score 691 · Answer 13 · 2026-03-25 11:06:38

691

Views

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

Published on 25 Mar 2026 - 11:06

score 567 · Answer 14 · 2019-04-09 16:55:00

567

Views

$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.

Published on 09 Apr 2019 - 16:55

score 160 · Answer 15 · 2026-03-25 01:25:37

160

Views

Chebotarev's theorem on cyclotomic extensions.

Published on 25 Mar 2026 - 1:25

List Question

A question on finite normal extension

Galois correspondence and invariant fields of L of $f(x)=x^4-2x^2-2$

Let k⊆K⊆E fields and if E/k is a finite extension, the E/K and K/k are also finite extensions.

Simple extension and the number of intermediate fields

$K$ cannot have subfields $k'$ and $k''$ such $k' \cong \mathbb{Q}$ and $k'' \cong \mathbb{F}_{p}$ where $p$ is some prime.

Galois group of $\mathbb{Q}(\sqrt[5]{3}):\mathbb{Q}$

confusion about Galois correspondence

Galois group of $\mathbb{Q}(\sqrt[5]{3},\zeta):\mathbb{Q}$

Galois group of a quintic with 3 real roots. How to conclude that there's one cycle of order 5?

Is there a standard notation for the Galois group of a polynomial?

Find the Galois group of $x^5-6x+3$ over $\mathbb{Q}$

Efficiently calculating the Galois group of $p(x)=x^4+4x^2-2$

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.

Chebotarev's theorem on cyclotomic extensions.

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