Question

If $F \subset E$ is Galois and there is a subfield of $E$ thats not normal, describe and find number of subfields

score 66 · Answer 1 · 2018-05-06 14:23:17

66

Views

If $F \subset E$ is Galois and there is a subfield of $E$ thats not normal, describe and find number of subfields

Published on 06 May 2018 - 14:23

score 456 · Answer 2 · 2018-05-06 17:04:15

456

Views

Galois group is simple implies subgroup of $A_n$

Published on 06 May 2018 - 17:04

score 91 · Answer 3 · 2026-03-25 23:51:42

91

Views

Example of field extensions

Published on 25 Mar 2026 - 23:51

score 125 · Answer 4 · 2018-05-06 20:40:06

125

Views

Normal closures of finite dimensional field extensions (existence, uniqueness, example)

Published on 06 May 2018 - 20:40

score 34 · Answer 5 · 2018-05-07 00:45:03

34

Views

A polynomial over $A[z]/(z^2-a)$ can be "completed" to a polynomial over $A$

Published on 07 May 2018 - 0:45

score 66 · Answer 6 · 2018-05-07 03:28:05

66

Views

Show one can get a finite Galois extension

Published on 07 May 2018 - 3:28

score 126 · Answer 7 · 2026-03-22 17:59:53

126

Views

What is the Galois group of some characteristic polynomial.

Published on 22 Mar 2026 - 17:59

score 219 · Answer 8 · 2026-03-25 01:16:58

219

Views

Galois groups and groups of Dirichlet characters

Published on 25 Mar 2026 - 1:16

score 170 · Answer 9 · 2018-05-07 12:41:07

170

Views

Prime decomposition in $\mathbb{Q}(\sqrt2 + \sqrt3)$

Published on 07 May 2018 - 12:41

score 126 · Answer 10 · 2018-05-07 14:05:01

126

Views

Open subgroups of Galois group with restricted ramification

Published on 07 May 2018 - 14:05

score 65 · Answer 11 · 2018-05-07 15:52:15

65

Views

Finding generating set for $\operatorname{Gal}_\mathbb{Q}f$

Published on 07 May 2018 - 15:52

score 153 · Answer 12 · 2018-05-07 17:09:34

153

Views

Proving the number of real roots of a cubic polynomial corresponds to the discriminant using Galois Theory

Published on 07 May 2018 - 17:09

score 625 · Answer 13 · 2026-03-27 07:14:45

625

Views

Clarification on proof that $\mathbb Q (\zeta _ m) \cap \mathbb Q(\zeta_n) = \mathbb Q$ when $\gcd(m,n) = 1$

Published on 27 Mar 2026 - 7:14

score 1.5k · Answer 14 · 2026-03-26 17:13:34

1.5k

Views

Twists of an Elliptic Curve over Finite Fields

Published on 26 Mar 2026 - 17:13

score 563 · Answer 15 · 2026-03-27 07:17:20

563

Views

Show Galois group of $f(t) = t^5 - 3$ over $\mathbb Q$ is solvable

Published on 27 Mar 2026 - 7:17

List Question

If $F \subset E$ is Galois and there is a subfield of $E$ thats not normal, describe and find number of subfields

Galois group is simple implies subgroup of $A_n$

Example of field extensions

Normal closures of finite dimensional field extensions (existence, uniqueness, example)

A polynomial over $A[z]/(z^2-a)$ can be "completed" to a polynomial over $A$

Show one can get a finite Galois extension

What is the Galois group of some characteristic polynomial.

Galois groups and groups of Dirichlet characters

Prime decomposition in $\mathbb{Q}(\sqrt2 + \sqrt3)$

Open subgroups of Galois group with restricted ramification

Finding generating set for $\operatorname{Gal}_\mathbb{Q}f$

Proving the number of real roots of a cubic polynomial corresponds to the discriminant using Galois Theory

Clarification on proof that $\mathbb Q (\zeta _ m) \cap \mathbb Q(\zeta_n) = \mathbb Q$ when $\gcd(m,n) = 1$

Twists of an Elliptic Curve over Finite Fields

Show Galois group of $f(t) = t^5 - 3$ over $\mathbb Q$ is solvable

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