Question

The Galois group of $x^{4}-a$ over $\mathbb{Q}$ where $a$ is any integer $\neq 0$, $\neq \pm 1$ and is square free.

score 449 · Answer 1 · 2018-04-07 09:40:11

449

Views

The Galois group of $x^{4}-a$ over $\mathbb{Q}$ where $a$ is any integer $\neq 0$, $\neq \pm 1$ and is square free.

Published on 07 Apr 2018 - 9:40

score 479 · Answer 2 · 2018-04-08 02:26:58

479

Views

Find the Galois group of $x^{4}-t$ over $\mathbb{R}(t)$, where $t$ is transcendental over the complex number $\mathbb{C}$

Published on 08 Apr 2018 - 2:26

score 86 · Answer 3 · 2026-03-25 22:26:52

86

Views

If $a$ and $b$ are elements of a finite field $k$, then $f(x)$ must have a root in $k$

Published on 25 Mar 2026 - 22:26

score 509 · Answer 4 · 2026-03-23 02:32:18

509

Views

Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?

Published on 23 Mar 2026 - 2:32

score 498 · Answer 5 · 2026-03-25 09:49:30

498

Views

Galois group as permutations of roots

Published on 25 Mar 2026 - 9:49

score 1.1k · Answer 6 · 2026-03-25 12:28:21

1.1k

Views

Galois Group of splitting field of $x^4 - x -1$ over $\mathbb{Q}$?

Published on 25 Mar 2026 - 12:28

score 113 · Answer 7 · 2026-03-25 08:54:00

113

Views

Help with proof that $[\mathcal{O}_K/\mathfrak{B}_i^{e_i}:\mathbb{Z}/p\mathbb{Z}] = e_i[\mathcal{O}_K/\mathfrak{B}_i:\mathbb{Z}/p\mathbb{Z}]$

Published on 25 Mar 2026 - 8:54

score 110 · Answer 8 · 2018-04-09 12:13:57

110

Views

What is the significance of 3-transitive Galois group

Published on 09 Apr 2018 - 12:13

score 394 · Answer 9 · 2026-03-25 07:44:48

394

Views

Infinite degree of the field of totally p-adic numbers

Published on 25 Mar 2026 - 7:44

score 87 · Answer 10 · 2018-04-10 17:18:08

87

Views

Splitting field of $x^{n} - a$ over $\mathbb{Q}$, where $a > 0$ and $a \in \mathbb{Q}$

Published on 10 Apr 2018 - 17:18

score 565 · Answer 11 · 2018-04-10 23:31:23

565

Views

Question on irreducibility of $x^{nm}-a$ when $n$ and $m$ are coprime

Published on 10 Apr 2018 - 23:31

score 1.4k · Answer 12 · 2026-03-25 17:40:45

1.4k

Views

Galois Group of $x^p-1$ cyclic

Published on 25 Mar 2026 - 17:40

score 1.1k · Answer 13 · 2026-03-25 16:02:18

1.1k

Views

Which roots of irreducible quartic polynomials are constructible by compass and straightedge?

Published on 25 Mar 2026 - 16:02

score 173 · Answer 14 · 2026-03-25 23:52:30

173

Views

How many elements in a field of size $3^4 (81)$ have multiplicative order $20$?

Published on 25 Mar 2026 - 23:52

score 925 · Answer 15 · 2018-04-11 12:47:09

925

Views

The Galois group is $\mathbb{Z_{4}}$ if and only if $\frac{\alpha}{\beta}-\frac{\beta}{\alpha}\in\mathbb{Q}$

Published on 11 Apr 2018 - 12:47

List Question

The Galois group of $x^{4}-a$ over $\mathbb{Q}$ where $a$ is any integer $\neq 0$, $\neq \pm 1$ and is square free.

Find the Galois group of $x^{4}-t$ over $\mathbb{R}(t)$, where $t$ is transcendental over the complex number $\mathbb{C}$

If $a$ and $b$ are elements of a finite field $k$, then $f(x)$ must have a root in $k$

Is the image of $\Phi_n(x) \in \mathbb{Z}[x]$ in $\mathbb{F}_q[x]$ still a cyclotomic polynomial?

Galois group as permutations of roots

Galois Group of splitting field of $x^4 - x -1$ over $\mathbb{Q}$?

Help with proof that $[\mathcal{O}_K/\mathfrak{B}_i^{e_i}:\mathbb{Z}/p\mathbb{Z}] = e_i[\mathcal{O}_K/\mathfrak{B}_i:\mathbb{Z}/p\mathbb{Z}]$

What is the significance of 3-transitive Galois group

Infinite degree of the field of totally p-adic numbers

Splitting field of $x^{n} - a$ over $\mathbb{Q}$, where $a > 0$ and $a \in \mathbb{Q}$

Question on irreducibility of $x^{nm}-a$ when $n$ and $m$ are coprime

Galois Group of $x^p-1$ cyclic

Which roots of irreducible quartic polynomials are constructible by compass and straightedge?

How many elements in a field of size $3^4 (81)$ have multiplicative order $20$?

The Galois group is $\mathbb{Z_{4}}$ if and only if $\frac{\alpha}{\beta}-\frac{\beta}{\alpha}\in\mathbb{Q}$

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