Question

Charactristic polynomial of a F-linear transformation with respect to Galois group

score 210 · Answer 1 · 2014-05-22 17:25:32

210

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Charactristic polynomial of a F-linear transformation with respect to Galois group

Published on 22 May 2014 - 17:25

score 786 · Answer 2 · 2026-03-30 08:57:39

786

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Prove for $a,b \in \mathbb{F}_{p^n}$, if $p(x) = x^3 + ax +b$ is irreducible, then $-4a^3 - 27b^2$ is a square in $\mathbb{F}_{p^n}$.

Published on 30 Mar 2026 - 8:57

score 180 · Answer 3 · 2014-05-23 07:57:52

180

Views

$\cos{nx}=p(\cos{x})$, general formula for $p$?

Published on 23 May 2014 - 7:57

score 299 · Answer 4 · 2026-03-27 22:55:19

299

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Galois Group of a cubic polynomial

Published on 27 Mar 2026 - 22:55

score 366 · Answer 5 · 2026-03-29 08:13:42

366

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Cubic polynomial - radical expression of roots

Published on 29 Mar 2026 - 8:13

score 94 · Answer 6 · 2014-05-23 19:12:32

94

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Elements in one Galois extension that act trivially on another Galois extension

Published on 23 May 2014 - 19:12

score 1.1k · Answer 7 · 2014-05-24 16:43:55

1.1k

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Let $F/\mathbb{Q}$ be a degree 4 extension, NOT Galois. Prove that the Galois closure of $F$ has Galois group either $S_4, A_4$ or $D_8$.

Published on 24 May 2014 - 16:43

score 58 · Answer 8 · 2014-05-24 17:18:41

58

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Galois theory in a different setting

Published on 24 May 2014 - 17:18

score 1.4k · Answer 9 · 2026-04-01 20:54:46

1.4k

Views

Galois group - extend homomorphism to automorphism

Published on 01 Apr 2026 - 20:54

score 1.5k · Answer 10 · 2014-05-25 05:45:51

1.5k

Views

Fixed Field of Automorphisms of $k(x)$

Published on 25 May 2014 - 5:45

score 244 · Answer 11 · 2014-05-26 00:23:42

244

Views

Counterexamples (I assume) on field extensions

Published on 26 May 2014 - 0:23

score 253 · Answer 12 · 2014-05-26 00:24:56

253

Views

Are there relations among Frobenii?

Published on 26 May 2014 - 0:24

score 321 · Answer 13 · 2014-05-26 18:25:52

321

Views

Constructing Galois extensions.

Published on 26 May 2014 - 18:25

score 542 · Answer 14 · 2014-05-27 03:00:12

542

Views

Show field extension is Galois via constructing separable polynomial

Published on 27 May 2014 - 3:00

score 85 · Answer 15 · 2026-03-27 22:52:49

85

Views

Why is $x^2-2ux+1$, where $u = \cos(\frac{2\pi}{n})$, irreducible in $\mathbb Q(u)$?

Published on 27 Mar 2026 - 22:52

List Question

Charactristic polynomial of a F-linear transformation with respect to Galois group

Prove for $a,b \in \mathbb{F}_{p^n}$, if $p(x) = x^3 + ax +b$ is irreducible, then $-4a^3 - 27b^2$ is a square in $\mathbb{F}_{p^n}$.

$\cos{nx}=p(\cos{x})$, general formula for $p$?

Galois Group of a cubic polynomial

Cubic polynomial - radical expression of roots

Elements in one Galois extension that act trivially on another Galois extension

Let $F/\mathbb{Q}$ be a degree 4 extension, NOT Galois. Prove that the Galois closure of $F$ has Galois group either $S_4, A_4$ or $D_8$.

Galois theory in a different setting

Galois group - extend homomorphism to automorphism

Fixed Field of Automorphisms of $k(x)$

Counterexamples (I assume) on field extensions

Are there relations among Frobenii?

Constructing Galois extensions.

Show field extension is Galois via constructing separable polynomial

Why is $x^2-2ux+1$, where $u = \cos(\frac{2\pi}{n})$, irreducible in $\mathbb Q(u)$?

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