List questions from galois-extensions

Published on 10 Apr 2026 - 17:05

73

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Computing Order of Galois Groups

Published on 13 Apr 2026 - 15:00

64

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Difficulty understanding a concept used

Published on 14 Apr 2026 - 23:43

60

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Intermediate Subfields

Published on 08 Apr 2026 - 11:24

119

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Explanation behind $\text{Gal}(K/K^H)=H$.

Published on 11 Apr 2026 - 16:09

104

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Understanding the Galois Extension

Published on 09 Apr 2026 - 13:51

76

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Can Kummer theory - there exists some $\gamma$, $L=K(\gamma^{1/n})$ - really be applied to any abelian extension $L/K$ (in characteristic zero, say)?

Published on 11 May 2026 - 3:17

41

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Explicit computation of the diameter of a point in the algebraic closure

Published on 13 Apr 2026 - 3:12

56

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Showing the Krull topology is the same as the categorical limit topology of (infinite) Galois extensions - is my solution correct?

Published on 14 Apr 2026 - 12:43

69

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If completions are equal for any prime then the fields are equal.

Published on 15 Apr 2026 - 3:57

162

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Relationship between the conductor of an extension $L/K$ and that of the Dirichlet's character on $Gal(L/K)$

Published on 13 Apr 2026 - 7:25

212

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The Galois group $Gal(\mathbb{Q}[\sqrt{p_1}, \dots , \sqrt{p_n}] | \mathbb{Q})$, $p_1, \dots , p_n$ prime integers, has $2^n-1$ subgroups of index $2$

Published on 17 Apr 2026 - 14:04

60

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The splitting field on $\mathbb{Q}$ of $x^4+10x^2+5$ is $\mathbb{Q}[i\sqrt{5-2\sqrt{5}}]$

Published on 16 Apr 2026 - 18:12

47

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Request for reference books, articles, papers on the topic topic of Non Abelian Kummer Extensions.

Published on 16 Apr 2026 - 1:42

165

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Finding Galois group of polynomial

Published on 12 Apr 2026 - 11:57

List Question

Galois Group of the minimal polynomial of

Computing Order of Galois Groups

Difficulty understanding a concept used

Intermediate Subfields

Explanation behind $\text{Gal}(K/K^H)=H$.

Understanding the Galois Extension

Can Kummer theory - there exists some $\gamma$, $L=K(\gamma^{1/n})$ - really be applied to any abelian extension $L/K$ (in characteristic zero, say)?

Explicit computation of the diameter of a point in the algebraic closure

Showing the Krull topology is the same as the categorical limit topology of (infinite) Galois extensions - is my solution correct?

If completions are equal for any prime then the fields are equal.

Relationship between the conductor of an extension $L/K$ and that of the Dirichlet's character on $Gal(L/K)$

The Galois group $Gal(\mathbb{Q}[\sqrt{p_1}, \dots , \sqrt{p_n}] | \mathbb{Q})$, $p_1, \dots , p_n$ prime integers, has $2^n-1$ subgroups of index $2$

The splitting field on $\mathbb{Q}$ of $x^4+10x^2+5$ is $\mathbb{Q}[i\sqrt{5-2\sqrt{5}}]$

Request for reference books, articles, papers on the topic topic of Non Abelian Kummer Extensions.

Finding Galois group of polynomial

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