Question

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

score 35 · Answer 1 · 2026-03-30 02:24:11

35

Views

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

Published on 30 Mar 2026 - 2:24

score 480 · Answer 2 · 2026-03-26 10:43:34

480

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 26 Mar 2026 - 10:43

score 112 · Answer 3 · 2021-07-20 04:06:35

112

Views

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

Published on 20 Jul 2021 - 4:06

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 80 · Answer 5 · 2021-07-20 12:59:40

80

Views

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

Published on 20 Jul 2021 - 12:59

score 205 · Answer 6 · 2021-07-23 17:50:10

205

Views

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

Published on 23 Jul 2021 - 17:50

score 49 · Answer 7 · 2021-07-27 21:21:06

49

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 27 Jul 2021 - 21:21

score 57 · Answer 8 · 2026-03-26 11:01:31

57

Views

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

Published on 26 Mar 2026 - 11:01

score 79 · Answer 9 · 2021-08-01 11:43:35

79

Views

Computing a certain Galois group

Published on 01 Aug 2021 - 11:43

score 67 · Answer 10 · 2021-08-06 21:15:59

67

Views

Two elements are not equal by using algebraic independent trick

Published on 06 Aug 2021 - 21:15

score 81 · Answer 11 · 2021-08-09 20:32:44

81

Views

Not surjective function by using algebra tools

Published on 09 Aug 2021 - 20:32

score 125 · Answer 12 · 2021-08-14 03:15:17

125

Views

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

Published on 14 Aug 2021 - 3:15

score 38 · Answer 13 · 2021-08-19 14:59:20

38

Views

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

Published on 19 Aug 2021 - 14:59

score 231 · Answer 14 · 2021-09-18 15:51:20

231

Views

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

Published on 18 Sep 2021 - 15:51

score 101 · Answer 15 · 2021-09-18 19:55:30

101

Views

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

Published on 18 Sep 2021 - 19:55

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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