Question

Tower of galois extensions. Prove that $\mathbb Q(2^{1/3})$ is not contained in $K_n$

score 124 · Answer 1 · 2026-03-25 23:52:18

124

Views

Tower of galois extensions. Prove that $\mathbb Q(2^{1/3})$ is not contained in $K_n$

Published on 25 Mar 2026 - 23:52

score 279 · Answer 2 · 2019-07-01 09:08:58

279

Views

If $E/\mathbb Q$ is a Galois extension of odd degree $n$, then $E\subseteq \mathbb R$

Published on 01 Jul 2019 - 9:08

score 154 · Answer 3 · 2019-07-01 12:12:23

154

Views

If $E/F$ is Galois of degree 4 with $\sqrt{-1}\in F$ then $E=F(\sqrt[4]{a})$ or $E=F(\sqrt{a}, \sqrt{b})$

Published on 01 Jul 2019 - 12:12

score 406 · Answer 4 · 2019-07-13 05:40:08

406

Views

Is there a way to find the subfields of a Galois extension without knowing the subgroup structure of the corresponding Galois group?

Published on 13 Jul 2019 - 5:40

score 70 · Answer 5 · 2019-07-18 16:18:02

70

Views

Find a field extension $E/\mathbb{F}_7$ of degree $3$

Published on 18 Jul 2019 - 16:18

score 209 · Answer 6 · 2026-03-25 01:28:51

209

Views

A faster way to find the quadratic extensions of a field extension?

Published on 25 Mar 2026 - 1:28

score 641 · Answer 7 · 2026-03-25 20:36:22

641

Views

Find Galois group of $x^3+x^2-2x-1\in\mathbb{Q}[x]$

Published on 25 Mar 2026 - 20:36

score 171 · Answer 8 · 2019-07-25 02:45:15

171

Views

Constructing Galois Extensions of Desired Degree

Published on 25 Jul 2019 - 2:45

score 516 · Answer 9 · 2026-03-26 04:30:21

516

Views

Extending Galois and Cyclotomic Fields

Published on 26 Mar 2026 - 4:30

score 149 · Answer 10 · 2019-07-28 01:32:40

149

Views

Is there a difference between the Galois group of $K/F$ and the Galois group of $E/K$ where $K$ is an intermediate field?

Published on 28 Jul 2019 - 1:32

score 392 · Answer 11 · 2026-03-26 20:49:06

392

Views

Artin-Schreier tower

Published on 26 Mar 2026 - 20:49

score 900 · Answer 12 · 2026-03-26 01:11:41

900

Views

Galois action on the character group of a torus

Published on 26 Mar 2026 - 1:11

score 97 · Answer 13 · 2019-08-13 13:26:19

97

Views

Roots of a projective polynomial

Published on 13 Aug 2019 - 13:26

score 237 · Answer 14 · 2019-08-14 09:11:02

237

Views

find $\alpha \in \mathbb{\overline{Q}}$ such that $\operatorname{Gal}(\mathbb{Q}(\alpha)/\mathbb{Q}) \cong \mathbb{Z}_5$

Published on 14 Aug 2019 - 9:11

score 1k · Answer 15 · 2019-09-06 06:49:37

1k

Views

Fixed field of an Automorphism

Published on 06 Sep 2019 - 6:49

List Question

Tower of galois extensions. Prove that $\mathbb Q(2^{1/3})$ is not contained in $K_n$

If $E/\mathbb Q$ is a Galois extension of odd degree $n$, then $E\subseteq \mathbb R$

If $E/F$ is Galois of degree 4 with $\sqrt{-1}\in F$ then $E=F(\sqrt[4]{a})$ or $E=F(\sqrt{a}, \sqrt{b})$

Is there a way to find the subfields of a Galois extension without knowing the subgroup structure of the corresponding Galois group?

Find a field extension $E/\mathbb{F}_7$ of degree $3$

A faster way to find the quadratic extensions of a field extension?

Find Galois group of $x^3+x^2-2x-1\in\mathbb{Q}[x]$

Constructing Galois Extensions of Desired Degree

Extending Galois and Cyclotomic Fields

Is there a difference between the Galois group of $K/F$ and the Galois group of $E/K$ where $K$ is an intermediate field?

Artin-Schreier tower

Galois action on the character group of a torus

Roots of a projective polynomial

find $\alpha \in \mathbb{\overline{Q}}$ such that $\operatorname{Gal}(\mathbb{Q}(\alpha)/\mathbb{Q}) \cong \mathbb{Z}_5$

Fixed field of an Automorphism

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