Question

Prove that $[ \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}]=8.$

score 944 · Answer 1 · 2026-03-25 21:01:33

944

Views

Prove that $[ \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}]=8.$

Published on 25 Mar 2026 - 21:01

score 169 · Answer 2 · 2026-02-23 01:23:03

169

Views

Is it true that $Gal(K/F)\cong S_{n_1}\times \cdots S_{n_k}$?

Published on 23 Feb 2026 - 1:23

score 223 · Answer 3 · 2019-01-31 18:06:24

223

Views

Proving that $[\mathbb{Q}(\sqrt{\sqrt{p+q}+\sqrt{q}},\sqrt{\sqrt{p+q}-\sqrt{q}}):\mathbb{Q}]=8$.

Published on 31 Jan 2019 - 18:06

score 107 · Answer 4 · 2019-02-02 23:26:31

107

Views

Show that $f(x)$ factors in $K[x]$(whether or not $K$ is contained in the Galois closure $L$ of $f(x)$).

Published on 02 Feb 2019 - 23:26

score 93 · Answer 5 · 2019-02-12 20:13:36

93

Views

Example of a Galois extension $L/\mathbb{Q}$ with $\text{Gal}(L/\mathbb{Q})\cong\mathbb{Z}_{4}$

Published on 12 Feb 2019 - 20:13

score 598 · Answer 6 · 2019-02-17 11:03:13

598

Views

Does $\mathbb{F}_9$ contain a 4th root of unity?

Published on 17 Feb 2019 - 11:03

score 42 · Answer 7 · 2026-03-25 01:26:01

42

Views

Question regarding Galois group and algebraic extensions

Published on 25 Mar 2026 - 1:26

score 1.4k · Answer 8 · 2026-03-25 22:26:08

1.4k

Views

Splitting field of separable polynomial is Galois extension

Published on 25 Mar 2026 - 22:26

score 24 · Answer 9 · 2019-03-03 03:48:30

24

Views

Meaning of a symbol regarding field.

Published on 03 Mar 2019 - 3:48

score 60 · Answer 10 · 2026-02-23 03:01:16

60

Views

$Gal(f)$ is cyclic of order $m$ for irreducible $f \in K[X]$ of degree $m$, where $K$ is a finite field

Published on 23 Feb 2026 - 3:01

score 428 · Answer 11 · 2026-03-25 11:04:32

428

Views

How to calculate the Galois group of $x^5+15x+12$?

Published on 25 Mar 2026 - 11:04

score 442 · Answer 12 · 2026-03-25 06:04:27

442

Views

Extension of degree 5 not obtained by adjoining a 5th root and whose normal closure contains a primitive 5th root of unity.

Published on 25 Mar 2026 - 6:04

score 248 · Answer 13 · 2019-03-10 23:28:31

248

Views

Method of showing maximal number of intermediate field extensions of a Galois extension with given degree

Published on 10 Mar 2019 - 23:28

score 54 · Answer 14 · 2019-03-13 04:49:41

54

Views

Let $M$ be a subfield of Complex field such that $M/\Bbb Q$ is a finite Galois extension

Published on 13 Mar 2019 - 4:49

score 164 · Answer 15 · 2019-03-16 17:02:32

164

Views

Show that the minimal polynomial over $F$ of each element of $E$ has only one distinct root.

Published on 16 Mar 2019 - 17:02

List Question

Prove that $[ \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}]=8.$

Is it true that $Gal(K/F)\cong S_{n_1}\times \cdots S_{n_k}$?

Proving that $[\mathbb{Q}(\sqrt{\sqrt{p+q}+\sqrt{q}},\sqrt{\sqrt{p+q}-\sqrt{q}}):\mathbb{Q}]=8$.

Show that $f(x)$ factors in $K[x]$(whether or not $K$ is contained in the Galois closure $L$ of $f(x)$).

Example of a Galois extension $L/\mathbb{Q}$ with $\text{Gal}(L/\mathbb{Q})\cong\mathbb{Z}_{4}$

Does $\mathbb{F}_9$ contain a 4th root of unity?

Question regarding Galois group and algebraic extensions

Splitting field of separable polynomial is Galois extension

Meaning of a symbol regarding field.

$Gal(f)$ is cyclic of order $m$ for irreducible $f \in K[X]$ of degree $m$, where $K$ is a finite field

How to calculate the Galois group of $x^5+15x+12$?

Extension of degree 5 not obtained by adjoining a 5th root and whose normal closure contains a primitive 5th root of unity.

Method of showing maximal number of intermediate field extensions of a Galois extension with given degree

Let $M$ be a subfield of Complex field such that $M/\Bbb Q$ is a finite Galois extension

Show that the minimal polynomial over $F$ of each element of $E$ has only one distinct root.

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