Question

Let $G$ be a finite group of automorphisms of $E$ and set $F=Fix(G)$, Then why is $E:F$ always separable?

score 61 · Answer 1 · 2026-02-23 03:01:21

61

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Let $G$ be a finite group of automorphisms of $E$ and set $F=Fix(G)$, Then why is $E:F$ always separable?

Published on 23 Feb 2026 - 3:01

score 38 · Answer 2 · 2026-04-01 03:00:05

38

Views

Is my line of reasoning correct for considering this fixed field as a simple extension over $GF(7)$?

Published on 01 Apr 2026 - 3:00

score 261 · Answer 3 · 2019-07-18 11:29:50

261

Views

Factorization of cubic $x^3 + x^2 - 2x -1\pmod p$

Published on 18 Jul 2019 - 11:29

score 71 · Answer 4 · 2026-03-28 04:34:54

71

Views

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

Published on 28 Mar 2026 - 4:34

score 201 · Answer 5 · 2019-07-18 18:17:44

201

Views

Let $\omega=\exp (2 \pi i / 3)$. Show that $\alpha=\omega+2\omega^{-1}$ is algebraic over $\mathbb{Q}$ and compute its minimal polynomial.

Published on 18 Jul 2019 - 18:17

score 63 · Answer 6 · 2026-04-01 03:00:05

63

Views

Question about degree of field extension in Galois Theory.

Published on 01 Apr 2026 - 3:00

score 179 · Answer 7 · 2026-04-01 03:01:57

179

Views

Exercise on the Primitive Element theorem.

Published on 01 Apr 2026 - 3:01

score 66 · Answer 8 · 2019-07-19 19:39:06

66

Views

Determine whether tha Galois Group can be $S_{4}$.

Published on 19 Jul 2019 - 19:39

score 74 · Answer 9 · 2019-07-20 17:54:36

Find a polynomial with splitting field $\mathbb{Q}(\sqrt[5]{3},\zeta)$ over $\mathbb{Q}$, where $\zeta$ is primitive 15-th root of unity.

score 55 · Answer 10 · 2019-07-21 20:13:45

55

Views

Galois Group Solve for radicals

Published on 21 Jul 2019 - 20:13

score 50 · Answer 11 · 2026-03-29 17:55:02

50

Views

Difficulty understanding this definition of Galois extensions

Published on 29 Mar 2026 - 17:55

score 210 · Answer 12 · 2026-03-30 19:01:36

210

Views

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

Published on 30 Mar 2026 - 19:01

score 214 · Answer 13 · 2019-07-23 11:33:51

214

Views

Primes of $\Bbb R[x]$ and Galois theory in terms of affine schemes

Published on 23 Jul 2019 - 11:33

score 41 · Answer 14 · 2026-03-25 07:44:48

41

Views

If $\text{Gal}(f)=D_{2017}$ for some $f\in\mathbb{Q}[x]$ then $f$ is solvable

Published on 25 Mar 2026 - 7:44

score 172 · Answer 15 · 2026-03-28 06:08:27

172

Views

Constructing Galois Extensions of Desired Degree

Published on 28 Mar 2026 - 6:08

List Question

Let $G$ be a finite group of automorphisms of $E$ and set $F=Fix(G)$, Then why is $E:F$ always separable?

Is my line of reasoning correct for considering this fixed field as a simple extension over $GF(7)$?

Factorization of cubic $x^3 + x^2 - 2x -1\pmod p$

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

Let $\omega=\exp (2 \pi i / 3)$. Show that $\alpha=\omega+2\omega^{-1}$ is algebraic over $\mathbb{Q}$ and compute its minimal polynomial.

Question about degree of field extension in Galois Theory.

Exercise on the Primitive Element theorem.

Determine whether tha Galois Group can be $S_{4}$.

Find a polynomial with splitting field $\mathbb{Q}(\sqrt[5]{3},\zeta)$ over $\mathbb{Q}$, where $\zeta$ is primitive 15-th root of unity.

Galois Group Solve for radicals

Difficulty understanding this definition of Galois extensions

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

Primes of $\Bbb R[x]$ and Galois theory in terms of affine schemes

If $\text{Gal}(f)=D_{2017}$ for some $f\in\mathbb{Q}[x]$ then $f$ is solvable

Constructing Galois Extensions of Desired Degree

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