Question

Is the Galois group of $\mathbb{Q} \left(\sqrt{5}+\sqrt{7}+i \right)$ isomorphic to $\mathbb{Z}_{2} \times \mathbb{Z}_{2} \times\mathbb{Z}_{2} $?

score 80 · Answer 1 · 2026-04-14 04:44:23

80

Views

Is the Galois group of $\mathbb{Q} \left(\sqrt{5}+\sqrt{7}+i \right)$ isomorphic to $\mathbb{Z}_{2} \times \mathbb{Z}_{2} \times\mathbb{Z}_{2} $?

Published on 14 Apr 2026 - 4:44

score 82 · Answer 2 · 2026-04-11 00:14:06

82

Views

Proving that the following equation does not have integer solutions

Published on 11 Apr 2026 - 0:14

score 46 · Answer 3 · 2026-04-13 05:14:34

46

Views

Is spliting field of $f(x) \in F[x]$ with $F$ a finite field also a finite field?

Published on 13 Apr 2026 - 5:14

score 57 · Answer 4 · 2026-04-14 21:42:17

57

Views

Proof verification: given a field $k$, any finite group can be represented as $\rm Gal(E/F)$ where $k\subset F\subset E$ and $E/F$ is Galois.

Published on 14 Apr 2026 - 21:42

score 56 · Answer 5 · 2026-04-12 08:34:26

56

Views

What am I misunderstanding in the definition of this subgroup?

Published on 12 Apr 2026 - 8:34

score 262 · Answer 6 · 2026-04-16 05:58:56

262

Views

Definition of field extensions: Can we talk about extensions like $\mathbb{F}_3(5)/\mathbb{F}_3$?

Published on 16 Apr 2026 - 5:58

score 60 · Answer 7 · 2026-04-09 00:05:53

60

Views

Odd field extensions, possible?

Published on 09 Apr 2026 - 0:05

score 60 · Answer 8 · 2026-04-14 09:07:53

60

Views

Does $a\neq b$ imply $a\otimes c\neq b\otimes c$ (when $c\neq 0$)?

Published on 14 Apr 2026 - 9:07

score 182 · Answer 9 · 2026-04-13 22:54:59

182

Views

Non-normal extension of Q

Published on 13 Apr 2026 - 22:54

score 125 · Answer 10 · 2026-04-15 21:25:11

125

Views

Given quintic polynomial $f$ - If ${\rm Gal}(f)$ has an element of order 3 then it is not solvable

Published on 15 Apr 2026 - 21:25

score 98 · Answer 11 · 2026-04-12 08:49:53

98

Views

Is the Field Norm Distributive over Multiplication?

Published on 12 Apr 2026 - 8:49

score 253 · Answer 12 · 2026-04-13 07:11:46

253

Views

Vector spaces and field extensions, and the Axiom of Choice

Published on 13 Apr 2026 - 7:11

score 55 · Answer 13 · 2026-03-25 12:35:05

55

Views

Splitting of $k[[x_1,...,x_n]]\to \bar k [[x_1,...,x_n]]$

Published on 25 Mar 2026 - 12:35

score 33 · Answer 14 · 2026-04-17 14:10:23

33

Views

If $\text{gcd}(m, n) = d$, true that for $a, m, n \in \mathbb{N}$, $\mathbb{Q}(a^{\frac{1}{n}}, a^{\frac{1}{m}}) = \mathbb{Q}(a^{\frac{d}{nm}})$?

Published on 17 Apr 2026 - 14:10

score 289 · Answer 15 · 2026-04-14 18:46:54

289

Views

"Complex numbers" in finite fields

Published on 14 Apr 2026 - 18:46

List Question

Is the Galois group of $\mathbb{Q} \left(\sqrt{5}+\sqrt{7}+i \right)$ isomorphic to $\mathbb{Z}_{2} \times \mathbb{Z}_{2} \times\mathbb{Z}_{2} $?

Proving that the following equation does not have integer solutions

Is spliting field of $f(x) \in F[x]$ with $F$ a finite field also a finite field?

Proof verification: given a field $k$, any finite group can be represented as $\rm Gal(E/F)$ where $k\subset F\subset E$ and $E/F$ is Galois.

What am I misunderstanding in the definition of this subgroup?

Definition of field extensions: Can we talk about extensions like $\mathbb{F}_3(5)/\mathbb{F}_3$?

Odd field extensions, possible?

Does $a\neq b$ imply $a\otimes c\neq b\otimes c$ (when $c\neq 0$)?

Non-normal extension of Q

Given quintic polynomial $f$ - If ${\rm Gal}(f)$ has an element of order 3 then it is not solvable

Is the Field Norm Distributive over Multiplication?

Vector spaces and field extensions, and the Axiom of Choice

Splitting of $k[[x_1,...,x_n]]\to \bar k [[x_1,...,x_n]]$

If $\text{gcd}(m, n) = d$, true that for $a, m, n \in \mathbb{N}$, $\mathbb{Q}(a^{\frac{1}{n}}, a^{\frac{1}{m}}) = \mathbb{Q}(a^{\frac{d}{nm}})$?

"Complex numbers" in finite fields

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