Question

Slick proof $\operatorname{Gal}(\mathbb Q[e^\frac{2\pi i}p, \sqrt[\leftroot{-2}\uproot{2}p]{2}]/\mathbb Q)\cong S_p$?

score 637 · Answer 1 · 2016-07-20 13:29:19

637

Views

Slick proof $\operatorname{Gal}(\mathbb Q[e^\frac{2\pi i}p, \sqrt[\leftroot{-2}\uproot{2}p]{2}]/\mathbb Q)\cong S_p$?

Published on 20 Jul 2016 - 13:29

score 459 · Answer 2 · 2016-07-20 22:45:18

459

Views

Calculating Galois group of $\mathbb Q(\cos \frac \pi 8)/\mathbb{Q}$

Published on 20 Jul 2016 - 22:45

score 454 · Answer 3 · 2026-04-04 16:34:25

454

Views

Geometric interpretation of primitive element theorem?

Published on 04 Apr 2026 - 16:34

score 330 · Answer 4 · 2016-07-22 01:45:22

330

Views

Let $E=\mathbb{Q}(2^{1/3})$. What is the normal closure of $E/E$?

Published on 22 Jul 2016 - 1:45

score 369 · Answer 5 · 2016-07-24 16:23:14

369

Views

Is a non-separable algebraic field extension $k \subset E$ normal if $\mathrm{Aut}_{E}(\bar{k})$ is a normal subgroup of $\mathrm{Aut}_{k}(\bar{k})$?

Published on 24 Jul 2016 - 16:23

score 88 · Answer 6 · 2016-07-27 00:59:03

If $F ⊂ \mathbb{C}$ and $α_1,\ldots,α_n$ ∈ $\mathbb{C}$ are algebraic over $F$, prove that $F(α_1, \ldots, α_n)$ is a simple extension of $F$.

score 104 · Answer 7 · 2016-07-30 04:27:56

104

Views

Doubt in Carathéodory's extension theorem

Published on 30 Jul 2016 - 4:27

score 110 · Answer 8 · 2016-07-30 11:43:05

110

Views

Some question on the separable extension.

Published on 30 Jul 2016 - 11:43

score 31 · Answer 9 · 2016-07-31 01:40:02

31

Views

Prove that there is a bijection given by $a_i → ρ(a_i)$.

Published on 31 Jul 2016 - 1:40

score 28 · Answer 10 · 2026-03-30 22:51:40

28

Views

Let $L$ be the splitting field of $f(x) = x^3 + 10x + 15$ over $\mathbb{Q}$, and $a_1$ (real), $a_2, a_3$ (complex conjugates) the roots of $f$

Published on 30 Mar 2026 - 22:51

score 71 · Answer 11 · 2026-04-02 13:25:24

71

Views

Normal extension of rational numbers with given Galois group

Published on 02 Apr 2026 - 13:25

score 122 · Answer 12 · 2016-08-03 19:50:26

122

Views

Understanding how tower extension field arithmetic works

Published on 03 Aug 2016 - 19:50

score 181 · Answer 13 · 2016-08-04 04:39:16

181

Views

Minimal Polynomial over an extension of $\mathbb Q$ Comp Question

Published on 04 Aug 2016 - 4:39

score 53 · Answer 14 · 2016-08-04 16:23:35

53

Views

Question about group $Aut(F/K)$

Published on 04 Aug 2016 - 16:23

score 31 · Answer 15 · 2016-08-05 12:42:13

31

Views

Extension of fields - Number of elements

Published on 05 Aug 2016 - 12:42

List Question

Slick proof $\operatorname{Gal}(\mathbb Q[e^\frac{2\pi i}p, \sqrt[\leftroot{-2}\uproot{2}p]{2}]/\mathbb Q)\cong S_p$?

Calculating Galois group of $\mathbb Q(\cos \frac \pi 8)/\mathbb{Q}$

Geometric interpretation of primitive element theorem?

Let $E=\mathbb{Q}(2^{1/3})$. What is the normal closure of $E/E$?

Is a non-separable algebraic field extension $k \subset E$ normal if $\mathrm{Aut}_{E}(\bar{k})$ is a normal subgroup of $\mathrm{Aut}_{k}(\bar{k})$?

If $F ⊂ \mathbb{C}$ and $α_1,\ldots,α_n$ ∈ $\mathbb{C}$ are algebraic over $F$, prove that $F(α_1, \ldots, α_n)$ is a simple extension of $F$.

Doubt in Carathéodory's extension theorem

Some question on the separable extension.

Prove that there is a bijection given by $a_i → ρ(a_i)$.

Let $L$ be the splitting field of $f(x) = x^3 + 10x + 15$ over $\mathbb{Q}$, and $a_1$ (real), $a_2, a_3$ (complex conjugates) the roots of $f$

Normal extension of rational numbers with given Galois group

Understanding how tower extension field arithmetic works

Minimal Polynomial over an extension of $\mathbb Q$ Comp Question

Question about group $Aut(F/K)$

Extension of fields - Number of elements

Trending Questions

Popular # Hahtags

Popular Questions