Question

$Gal(LM/K)$ isomorphic to $ \{ (\sigma , \tau) \in Gal(L/K) \times Gal(M/K) : \sigma |_{L \cap M} = \tau |_{L \cap M} \} $

score 89 · Answer 1 · 2026-02-23 08:28:27

89

Views

$Gal(LM/K)$ isomorphic to $ \{ (\sigma , \tau) \in Gal(L/K) \times Gal(M/K) : \sigma |_{L \cap M} = \tau |_{L \cap M} \} $

Published on 23 Feb 2026 - 8:28

score 66 · Answer 2 · 2023-12-17 12:00:39

66

Views

$E = \mathbb{Q}( \sqrt{p_1}, . . . , \sqrt{p_n})$. Show that $Gal(E/\mathbb{Q}) \cong (\mathbb{Z}/2\mathbb{Z})^n$

Published on 17 Dec 2023 - 12:00

score 80 · Answer 3 · 2023-12-20 08:59:26

80

Views

If $E/F$ is a Galois extension, $Gal(E/F)$ is finite, and $K$ is an intermediate field that is a degree 2 extension from $F$, prove $K/F$ is Galois

Published on 20 Dec 2023 - 8:59

score 60 · Answer 4 · 2026-03-25 17:52:57

60

Views

Construct primitive element for intermediate field of cyclotomic field extension

Published on 25 Mar 2026 - 17:52

score 123 · Answer 5 · 2023-12-23 18:36:43

123

Views

$f\in\mathbb{Q}[x]$ is irreducible in $\mathbb{Q}[x]$ and the Galois group of $f$ has order 99 , what is the degree of $f$.

Published on 23 Dec 2023 - 18:36

score 50 · Answer 6 · 2024-01-12 23:16:57

50

Views

What is known of this problem similar to the inverse Galois problem? Galois groups of $\mathbb{Q}(X)/\mathbb{Q}(h(X))$ for $h \in \mathbb{Q}(X)$

Published on 12 Jan 2024 - 23:16

score 31 · Answer 7 · 2026-03-26 11:05:04

31

Views

density of $\langle \textit{Frobenius}\rangle$ in $Gal(L/K)$

Published on 26 Mar 2026 - 11:05

score 22 · Answer 8 · 2024-02-01 19:39:08

22

Views

Trascendental extension over the complex field

Published on 01 Feb 2024 - 19:39

score 82 · Answer 9 · 2026-03-25 19:25:16

82

Views

How to compute the different ideal of the cyclotomic field extension $\mathbb{Q}(\zeta_p)/\mathbb{Q}$?

Published on 25 Mar 2026 - 19:25

score 61 · Answer 10 · 2024-02-15 11:38:59

61

Views

Construction of Type II optimal normal basis of $GF(2^n)$ over $GF(2)$

Published on 15 Feb 2024 - 11:38

score 25 · Answer 11 · 2026-03-26 11:04:58

25

Views

galois group of completions

Published on 26 Mar 2026 - 11:04

score 23 · Answer 12 · 2024-03-01 11:37:25

23

Views

Proof in The Galois Groups and Fundamental groups by Szamuely (lemma 3.4.2 )

Published on 01 Mar 2024 - 11:37

score 22 · Answer 13 · 2024-03-07 16:38:03

22

Views

Representatives of Quotient Group of Galois Groups

Published on 07 Mar 2024 - 16:38

score 48 · Answer 14 · 2026-03-26 13:51:29

48

Views

A question about the embedding from $\mathbb{Q}(\sqrt{2},\sqrt{3})$ to an algebraic closure of $\mathbb{Q}$

Published on 26 Mar 2026 - 13:51

score 52 · Answer 15 · 2024-03-10 10:33:28

52

Views

Some questions about the trace of $\alpha \in K$ from $K$ to $F$ where $K,F$ are fields

Published on 10 Mar 2024 - 10:33

List Question

$Gal(LM/K)$ isomorphic to $ \{ (\sigma , \tau) \in Gal(L/K) \times Gal(M/K) : \sigma |_{L \cap M} = \tau |_{L \cap M} \} $

$E = \mathbb{Q}( \sqrt{p_1}, . . . , \sqrt{p_n})$. Show that $Gal(E/\mathbb{Q}) \cong (\mathbb{Z}/2\mathbb{Z})^n$

If $E/F$ is a Galois extension, $Gal(E/F)$ is finite, and $K$ is an intermediate field that is a degree 2 extension from $F$, prove $K/F$ is Galois

Construct primitive element for intermediate field of cyclotomic field extension

$f\in\mathbb{Q}[x]$ is irreducible in $\mathbb{Q}[x]$ and the Galois group of $f$ has order 99 , what is the degree of $f$.

What is known of this problem similar to the inverse Galois problem? Galois groups of $\mathbb{Q}(X)/\mathbb{Q}(h(X))$ for $h \in \mathbb{Q}(X)$

density of $\langle \textit{Frobenius}\rangle$ in $Gal(L/K)$

Trascendental extension over the complex field

How to compute the different ideal of the cyclotomic field extension $\mathbb{Q}(\zeta_p)/\mathbb{Q}$?

Construction of Type II optimal normal basis of $GF(2^n)$ over $GF(2)$

galois group of completions

Proof in The Galois Groups and Fundamental groups by Szamuely (lemma 3.4.2 )

Representatives of Quotient Group of Galois Groups

A question about the embedding from $\mathbb{Q}(\sqrt{2},\sqrt{3})$ to an algebraic closure of $\mathbb{Q}$

Some questions about the trace of $\alpha \in K$ from $K$ to $F$ where $K,F$ are fields

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