Question

Prove that the Galois group of $f\left(x\right)$ over $\mathbb{Q}$ is not a simple group.

score 81 · Answer 1 · 2026-03-26 20:41:08

81

Views

Prove that the Galois group of $f\left(x\right)$ over $\mathbb{Q}$ is not a simple group.

Published on 26 Mar 2026 - 20:41

score 838 · Answer 2 · 2019-03-17 23:22:19

838

Views

Is the extension $\mathbb{Q}(\sqrt{5},\sqrt{7})$ simple? If so/not, why?

Published on 17 Mar 2019 - 23:22

score 510 · Answer 3 · 2019-03-19 03:38:54

510

Views

Galois Group and Subfield lattice of $(x^2 - 7)(x^4 + x^3 + x^2 + x + 1)$ over $\mathbb{Q}$

Published on 19 Mar 2019 - 3:38

score 51 · Answer 4 · 2019-03-21 12:32:32

51

Views

Why a homomorphism from full Galois group of rationals cannot factor.

Published on 21 Mar 2019 - 12:32

score 1.5k · Answer 5 · 2026-02-23 02:59:19

1.5k

Views

How to compute a primitive element for the splitting field of $x^3-2 \in \Bbb{Q}[x]$?

Published on 23 Feb 2026 - 2:59

score 306 · Answer 6 · 2026-03-25 21:49:03

306

Views

Automorphism of $\mathbb{C}$ over a subfield $K$ of $\mathbb{C}$

Published on 25 Mar 2026 - 21:49

score 197 · Answer 7 · 2019-03-24 21:22:33

197

Views

The degree of extension

Published on 24 Mar 2019 - 21:22

score 263 · Answer 8 · 2019-03-26 14:51:09

263

Views

Let $K/E$ and $E/F$ be Galois extensions. If every $σ ∈ \text{Aut}(E/F)$ is the restriction of an element of $\text{Aut}(K/F)$, then $K/F$ is Galois.

Published on 26 Mar 2019 - 14:51

score 134 · Answer 9 · 2019-03-31 03:38:41

134

Views

Suppose $a,b\in E$ and $\sigma\in \textrm{Gal}(E/F)$ with $\sigma(a)=b$. Show that $a$ and $b$ have the same minimal polynomial in $F[x]$

Published on 31 Mar 2019 - 3:38

score 37 · Answer 10 · 2026-03-26 11:17:53

37

Views

If $K$ is a subfield of $\mathbb{C}$ then $K(\zeta)/K$ is Galois

Published on 26 Mar 2026 - 11:17

score 312 · Answer 11 · 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 63 · Answer 12 · 2019-04-10 23:06:19

Let $\alpha=2^{1/5}$ ,$\zeta=e^{2i\pi/5}$ and $K=\mathbb{Q}(\alpha\zeta)$, can the field automorphism of K be extended to an automorphism of C?

score 336 · Answer 13 · 2019-04-14 15:16:13

336

Views

My attempt at finding the Galois group of $E:\Bbb Q$, where $E$ is the splitting field of $x^3-5$

Published on 14 Apr 2019 - 15:16

score 188 · Answer 14 · 2026-03-25 17:39:36

188

Views

Group is soluble if and only if quotient is abelian

Published on 25 Mar 2026 - 17:39

score 364 · Answer 15 · 2026-03-25 01:27:15

364

Views

Find all subfields of $\mathbb{Q}(\mu_{24})$

Published on 25 Mar 2026 - 1:27

List Question

Prove that the Galois group of $f\left(x\right)$ over $\mathbb{Q}$ is not a simple group.

Is the extension $\mathbb{Q}(\sqrt{5},\sqrt{7})$ simple? If so/not, why?

Galois Group and Subfield lattice of $(x^2 - 7)(x^4 + x^3 + x^2 + x + 1)$ over $\mathbb{Q}$

Why a homomorphism from full Galois group of rationals cannot factor.

How to compute a primitive element for the splitting field of $x^3-2 \in \Bbb{Q}[x]$?

Automorphism of $\mathbb{C}$ over a subfield $K$ of $\mathbb{C}$

The degree of extension

Let $K/E$ and $E/F$ be Galois extensions. If every $σ ∈ \text{Aut}(E/F)$ is the restriction of an element of $\text{Aut}(K/F)$, then $K/F$ is Galois.

Suppose $a,b\in E$ and $\sigma\in \textrm{Gal}(E/F)$ with $\sigma(a)=b$. Show that $a$ and $b$ have the same minimal polynomial in $F[x]$

If $K$ is a subfield of $\mathbb{C}$ then $K(\zeta)/K$ is Galois

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

Let $\alpha=2^{1/5}$ ,$\zeta=e^{2i\pi/5}$ and $K=\mathbb{Q}(\alpha\zeta)$, can the field automorphism of K be extended to an automorphism of C?

My attempt at finding the Galois group of $E:\Bbb Q$, where $E$ is the splitting field of $x^3-5$

Group is soluble if and only if quotient is abelian

Find all subfields of $\mathbb{Q}(\mu_{24})$

Trending Questions

Popular # Hahtags

Popular Questions