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 92 · Answer 1 · 2026-04-16 17:31:48

92

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 16 Apr 2026 - 17:31

score 68 · Answer 2 · 2026-04-16 13:43:38

68

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 16 Apr 2026 - 13:43

score 83 · Answer 3 · 2026-04-16 02:27:19

83

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 16 Apr 2026 - 2:27

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 126 · Answer 5 · 2026-04-16 16:20:27

126

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 16 Apr 2026 - 16:20

score 53 · Answer 6 · 2026-04-16 07:46:29

53

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 16 Apr 2026 - 7:46

score 33 · Answer 7 · 2026-04-13 07:41:11

33

Views

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

Published on 13 Apr 2026 - 7:41

score 25 · Answer 8 · 2026-04-11 07:50:22

25

Views

Trascendental extension over the complex field

Published on 11 Apr 2026 - 7:50

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 64 · Answer 10 · 2026-04-16 02:55:28

64

Views

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

Published on 16 Apr 2026 - 2:55

score 27 · Answer 11 · 2026-04-11 05:35:12

27

Views

galois group of completions

Published on 11 Apr 2026 - 5:35

score 26 · Answer 12 · 2026-04-14 04:32:31

26

Views

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

Published on 14 Apr 2026 - 4:32

score 25 · Answer 13 · 2026-04-09 19:04:49

25

Views

Representatives of Quotient Group of Galois Groups

Published on 09 Apr 2026 - 19:04

score 50 · Answer 14 · 2026-04-16 03:26:27

50

Views

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

Published on 16 Apr 2026 - 3:26

score 55 · Answer 15 · 2026-04-11 11:11:53

55

Views

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

Published on 11 Apr 2026 - 11:11

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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