Question

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

score 126 · Answer 1 · 2026-04-15 14:18:55

126

Views

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

Published on 15 Apr 2026 - 14:18

score 282 · Answer 2 · 2026-04-16 03:26:19

282

Views

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

Published on 16 Apr 2026 - 3:26

score 157 · Answer 3 · 2026-04-16 04:24:25

157

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 16 Apr 2026 - 4:24

score 409 · Answer 4 · 2026-04-13 02:32:33

409

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 Apr 2026 - 2:32

score 73 · Answer 5 · 2026-04-16 14:22:47

73

Views

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

Published on 16 Apr 2026 - 14:22

score 215 · Answer 6 · 2026-05-10 16:13:53

215

Views

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

Published on 10 May 2026 - 16:13

score 644 · Answer 7 · 2026-05-10 20:03:59

644

Views

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

Published on 10 May 2026 - 20:03

score 174 · Answer 8 · 2026-04-12 14:46:52

174

Views

Constructing Galois Extensions of Desired Degree

Published on 12 Apr 2026 - 14:46

score 518 · Answer 9 · 2026-04-09 10:54:50

518

Views

Extending Galois and Cyclotomic Fields

Published on 09 Apr 2026 - 10:54

score 152 · Answer 10 · 2026-04-13 10:41:32

152

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 13 Apr 2026 - 10:41

score 396 · Answer 11 · 2026-05-10 15:08:18

396

Views

Artin-Schreier tower

Published on 10 May 2026 - 15:08

score 902 · Answer 12 · 2026-04-14 07:06:42

902

Views

Galois action on the character group of a torus

Published on 14 Apr 2026 - 7:06

score 100 · Answer 13 · 2026-04-14 05:42:41

100

Views

Roots of a projective polynomial

Published on 14 Apr 2026 - 5:42

score 240 · Answer 14 · 2026-04-17 12:24:58

240

Views

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

Published on 17 Apr 2026 - 12:24

score 1k · Answer 15 · 2026-04-12 14:33:19

1k

Views

Fixed field of an Automorphism

Published on 12 Apr 2026 - 14:33

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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