Question

Is the normal closure of $L:K$ the same as the normal closure of $L:K(α)$?

score 56 · Answer 1 · 2018-06-21 22:20:21

56

Views

Is the normal closure of $L:K$ the same as the normal closure of $L:K(α)$?

Published on 21 Jun 2018 - 22:20

score 168 · Answer 2 · 2018-06-22 18:20:42

168

Views

If an extension is locally Galois, is it Galois?

Published on 22 Jun 2018 - 18:20

score 1.9k · Answer 3 · 2026-03-26 12:53:45

1.9k

Views

Prove that $GL_n(\mathbb{F}_p)$ contains an element of order $p^n-1$

Published on 26 Mar 2026 - 12:53

score 92 · Answer 4 · 2026-03-28 12:02:56

92

Views

How I can show that $\sqrt[3]{x}$ is separable over $\mathbb{Z}_{2}(x)$?

Published on 28 Mar 2026 - 12:02

score 161 · Answer 5 · 2018-06-23 14:03:17

161

Views

Is there an algebraic extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

Published on 23 Jun 2018 - 14:03

score 97 · Answer 6 · 2026-03-25 17:59:11

97

Views

Can $\mathrm{Aut}(\Bbb C)$ be turned into a profinite group?

Published on 25 Mar 2026 - 17:59

score 68 · Answer 7 · 2026-03-28 11:54:21

68

Views

Fundamental Theorem of Galois Theory and cyclic group of order $30$ (Proof verification)

Published on 28 Mar 2026 - 11:54

score 75 · Answer 8 · 2018-06-24 16:20:40

75

Views

$|\mathrm{Gal}(L/K)| = 105$ and subgroups $A,B \leq \mathrm{Gal}(L/K)$ with $|A| = 21$ and $|B| = 35$. Prove that $L^{A}\cap L^{B} = K$.

Published on 24 Jun 2018 - 16:20

score 98 · Answer 9 · 2026-03-25 15:26:57

98

Views

$\Theta =70$ degrees into seven angles $\Theta /7=10$ is not possible by euclids method

Published on 25 Mar 2026 - 15:26

score 190 · Answer 10 · 2018-06-26 15:49:50

190

Views

Show that every root of a polynomial is real (using Galois theory)

Published on 26 Jun 2018 - 15:49

score 445 · Answer 11 · 2018-06-26 17:53:08

445

Views

Determine $Gal(K/F)$ and find all the intermediate subfields of $K/F$.

Published on 26 Jun 2018 - 17:53

score 1.2k · Answer 12 · 2018-06-26 18:32:14

1.2k

Views

Let $K$ be a Galois extension of $F$ with $[K/F] = n$. If $p$ is a prime divisor of $n$, show that there is a subfield $L$ of $K$ with $[K:L] = p$

Published on 26 Jun 2018 - 18:32

score 669 · Answer 13 · 2026-03-25 13:13:30

669

Views

Order of splitting field of $x^5+8$

Published on 25 Mar 2026 - 13:13

score 52 · Answer 14 · 2018-06-27 16:56:14

52

Views

prove $2^{1/4}$ not in $Q(\xi)$

Published on 27 Jun 2018 - 16:56

score 233 · Answer 15 · 2018-06-27 17:14:01

233

Views

Prove that if $ \operatorname{Gal}(K/F) \simeq \Bbb{Z}/2\Bbb{Z}\times\Bbb{Z}/2\mathbb{Z}$, then $K = F(\sqrt{a},\sqrt{b})$ for some $a,b \in F$

Published on 27 Jun 2018 - 17:14

List Question

Is the normal closure of $L:K$ the same as the normal closure of $L:K(α)$?

If an extension is locally Galois, is it Galois?

Prove that $GL_n(\mathbb{F}_p)$ contains an element of order $p^n-1$

How I can show that $\sqrt[3]{x}$ is separable over $\mathbb{Z}_{2}(x)$?

Is there an algebraic extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

Can $\mathrm{Aut}(\Bbb C)$ be turned into a profinite group?

Fundamental Theorem of Galois Theory and cyclic group of order $30$ (Proof verification)

$|\mathrm{Gal}(L/K)| = 105$ and subgroups $A,B \leq \mathrm{Gal}(L/K)$ with $|A| = 21$ and $|B| = 35$. Prove that $L^{A}\cap L^{B} = K$.

$\Theta =70$ degrees into seven angles $\Theta /7=10$ is not possible by euclids method

Show that every root of a polynomial is real (using Galois theory)

Determine $Gal(K/F)$ and find all the intermediate subfields of $K/F$.

Let $K$ be a Galois extension of $F$ with $[K/F] = n$. If $p$ is a prime divisor of $n$, show that there is a subfield $L$ of $K$ with $[K:L] = p$

Order of splitting field of $x^5+8$

prove $2^{1/4}$ not in $Q(\xi)$

Prove that if $ \operatorname{Gal}(K/F) \simeq \Bbb{Z}/2\Bbb{Z}\times\Bbb{Z}/2\mathbb{Z}$, then $K = F(\sqrt{a},\sqrt{b})$ for some $a,b \in F$

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