Question

Why is the Galois closure of $K/F$ the composite of the Galois conjugates of $K$?

score 3.4k · Answer 1 · 2014-03-13 02:42:46

3.4k

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Why is the Galois closure of $K/F$ the composite of the Galois conjugates of $K$?

Published on 13 Mar 2014 - 2:42

score 975 · Answer 2 · 2014-03-13 16:47:08

975

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How to determine the density of the set of completely splitting primes for a finite extension?

Published on 13 Mar 2014 - 16:47

score 234 · Answer 3 · 2014-03-14 01:03:21

234

Views

Is the extension $\mathbb{Q}(\sqrt[m]{n})/\mathbb{Q}$ not Normal for $m > 1$ and $n$ square free?

Published on 14 Mar 2014 - 1:03

score 507 · Answer 4 · 2014-03-15 00:07:34

507

Views

Galois group of composite of Galois extensions

Published on 15 Mar 2014 - 0:07

score 1.1k · Answer 5 · 2014-03-15 06:30:37

1.1k

Views

Simple radical extension

Published on 15 Mar 2014 - 6:30

score 89 · Answer 6 · 2014-03-17 10:40:24

89

Views

Problem with understanding Sn is realizable over Q? help!!

Published on 17 Mar 2014 - 10:40

score 1.8k · Answer 7 · 2014-03-18 06:25:40

1.8k

Views

What are the subfields of $\mathbb{Q}(\sqrt{3},\sqrt[7]{5})$?

Published on 18 Mar 2014 - 6:25

score 1.2k · Answer 8 · 2014-03-19 03:17:44

1.2k

Views

normal extension of $\mathbb{Q}$

Published on 19 Mar 2014 - 3:17

score 297 · Answer 9 · 2014-03-19 13:50:56

297

Views

The fixed field of a galois group if the characteristic is $p$.

Published on 19 Mar 2014 - 13:50

score 619 · Answer 10 · 2026-03-27 15:07:35

619

Views

$p$-part of cyclotomic character

Published on 27 Mar 2026 - 15:07

score 141 · Answer 11 · 2026-04-01 20:56:30

141

Views

Precise Error Term in Chebotarev's Theorem

Published on 01 Apr 2026 - 20:56

score 117 · Answer 12 · 2014-03-20 22:54:05

117

Views

Number field theoretical analogue of Riemann's Existence Theorem

Published on 20 Mar 2014 - 22:54

score 636 · Answer 13 · 2026-03-27 14:59:05

636

Views

Reducibility of a Cyclotomic Polynomial under the ring homomorphism $\mathbb{Z} \rightarrow \mathbb{F}_p$

Published on 27 Mar 2026 - 14:59

score 63 · Answer 14 · 2014-03-21 23:14:20

63

Views

How are the two Galois groups are equal?

Published on 21 Mar 2014 - 23:14

score 2.8k · Answer 15 · 2014-03-22 05:34:09

2.8k

Views

Prove that the Galois group of $x^n-1$ is abelian over the rationals

Published on 22 Mar 2014 - 5:34

List Question

Why is the Galois closure of $K/F$ the composite of the Galois conjugates of $K$?

How to determine the density of the set of completely splitting primes for a finite extension?

Is the extension $\mathbb{Q}(\sqrt[m]{n})/\mathbb{Q}$ not Normal for $m > 1$ and $n$ square free?

Galois group of composite of Galois extensions

Simple radical extension

Problem with understanding Sn is realizable over Q? help!!

What are the subfields of $\mathbb{Q}(\sqrt{3},\sqrt[7]{5})$?

normal extension of $\mathbb{Q}$

The fixed field of a galois group if the characteristic is $p$.

$p$-part of cyclotomic character

Precise Error Term in Chebotarev's Theorem

Number field theoretical analogue of Riemann's Existence Theorem

Reducibility of a Cyclotomic Polynomial under the ring homomorphism $\mathbb{Z} \rightarrow \mathbb{F}_p$

How are the two Galois groups are equal?

Prove that the Galois group of $x^n-1$ is abelian over the rationals

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