Question

Hopf-Galois structures of cyclic type on a dihedral or quaternionic extension

score 37 · Answer 1 · 2026-04-15 21:37:16

37

Views

Hopf-Galois structures of cyclic type on a dihedral or quaternionic extension

Published on 15 Apr 2026 - 21:37

score 482 · Answer 2 · 2026-04-16 09:04:11

482

Views

$\mathbb{Q}(\alpha)$ extension of degree 3 is galois over $\mathbb{Q}$ if and only if discriminant of minimal polynomial of $\alpha$ is square.

Published on 16 Apr 2026 - 9:04

score 115 · Answer 3 · 2026-04-16 17:42:36

115

Views

Why doesn't "$S_n$ appears as a Galois group over $\Bbb{Q}$" wrap up the Inverse Galois Problem?

Published on 16 Apr 2026 - 17:42

score 22 · Answer 4 · 2026-03-26 09:50:05

22

Views

If $f(t,x)\in F_q(t)[x]$ is a Morse function, does this mean splitting field of $f(t,x)$ over $F_q(t)$ is a regular extension?

Published on 26 Mar 2026 - 9:50

score 83 · Answer 5 · 2026-04-16 10:58:01

83

Views

is $f(x) = 20x^5-35x^4+10x^3-1$ irreducible over $\Bbb Q [\sqrt{3}]$?

Published on 16 Apr 2026 - 10:58

score 208 · Answer 6 · 2026-04-16 08:49:44

208

Views

Galois group of $x^5-5x^3+4x+1 \in \mathbb{Q}[x] $

Published on 16 Apr 2026 - 8:49

score 52 · Answer 7 · 2026-04-15 02:48:08

52

Views

$L|_k$ be a finite Galois extension and $M,N$ are subfields containing $k$ such that $[M:k], [N:k]$ are powers of $2$. Is $[MN:k]$ power of $2$?

Published on 15 Apr 2026 - 2:48

score 59 · Answer 8 · 2026-04-10 14:37:32

59

Views

How can you specifically extend an automorphism from a quadratic field to one of a cyclotomic field?

Published on 10 Apr 2026 - 14:37

score 82 · Answer 9 · 2026-04-10 13:45:34

82

Views

Computing a certain Galois group

Published on 10 Apr 2026 - 13:45

score 70 · Answer 10 · 2026-04-12 10:21:46

70

Views

Two elements are not equal by using algebraic independent trick

Published on 12 Apr 2026 - 10:21

score 84 · Answer 11 · 2026-04-12 06:27:41

84

Views

Not surjective function by using algebra tools

Published on 12 Apr 2026 - 6:27

score 128 · Answer 12 · 2026-04-14 22:11:20

128

Views

Linearly disjoint family of fields $\{L_i \}_{i=1}^n$ over $K$

Published on 14 Apr 2026 - 22:11

score 41 · Answer 13 · 2026-04-16 13:28:32

41

Views

When are the extensions $L(S)/K$ and $L(S)/L$ totally ramified?

Published on 16 Apr 2026 - 13:28

score 234 · Answer 14 · 2026-04-11 08:49:59

234

Views

Galois extension of $p^2$ root of unity contains a subfield whose Galois group is $\mathbb{Z}/p\mathbb{Z}$.

Published on 11 Apr 2026 - 8:49

score 104 · Answer 15 · 2026-04-16 05:02:40

104

Views

why is $\sigma\tau\neq\tau\sigma$ in $\operatorname{Gal}(\mathbb{Q}(\sqrt[3] 2,\zeta_3)/\mathbb{Q})?$

Published on 16 Apr 2026 - 5:02

List Question

Hopf-Galois structures of cyclic type on a dihedral or quaternionic extension

$\mathbb{Q}(\alpha)$ extension of degree 3 is galois over $\mathbb{Q}$ if and only if discriminant of minimal polynomial of $\alpha$ is square.

Why doesn't "$S_n$ appears as a Galois group over $\Bbb{Q}$" wrap up the Inverse Galois Problem?

If $f(t,x)\in F_q(t)[x]$ is a Morse function, does this mean splitting field of $f(t,x)$ over $F_q(t)$ is a regular extension?

is $f(x) = 20x^5-35x^4+10x^3-1$ irreducible over $\Bbb Q [\sqrt{3}]$?

Galois group of $x^5-5x^3+4x+1 \in \mathbb{Q}[x] $

$L|_k$ be a finite Galois extension and $M,N$ are subfields containing $k$ such that $[M:k], [N:k]$ are powers of $2$. Is $[MN:k]$ power of $2$?

How can you specifically extend an automorphism from a quadratic field to one of a cyclotomic field?

Computing a certain Galois group

Two elements are not equal by using algebraic independent trick

Not surjective function by using algebra tools

Linearly disjoint family of fields $\{L_i \}_{i=1}^n$ over $K$

When are the extensions $L(S)/K$ and $L(S)/L$ totally ramified?

Galois extension of $p^2$ root of unity contains a subfield whose Galois group is $\mathbb{Z}/p\mathbb{Z}$.

why is $\sigma\tau\neq\tau\sigma$ in $\operatorname{Gal}(\mathbb{Q}(\sqrt[3] 2,\zeta_3)/\mathbb{Q})?$

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