Question

Take a galois group $Gal(K/\mathbb{Q})$ isomorphic to $C_{16}$. How many subfields $L$ exist such that $[K:L] = 4$?

score 50 · Answer 1 · 2026-04-17 15:21:11

50

Views

Take a galois group $Gal(K/\mathbb{Q})$ isomorphic to $C_{16}$. How many subfields $L$ exist such that $[K:L] = 4$?

Published on 17 Apr 2026 - 15:21

score 200 · Answer 2 · 2026-04-12 16:56:43

200

Views

Is element in infinitely generated field extension contained in finitely generated field extension?

Published on 12 Apr 2026 - 16:56

score 68 · Answer 3 · 2026-03-25 08:09:46

68

Views

Minimal polynomial of $\eta_4$ over $\mathbb{Q}(\eta_2)$.

Published on 25 Mar 2026 - 8:09

score 86 · Answer 4 · 2026-04-11 01:15:38

86

Views

A question regarding the definition of a quadratic field

Published on 11 Apr 2026 - 1:15

score 121 · Answer 5 · 2026-03-25 08:13:36

121

Views

Evaluate sum roots of unity $\zeta_{17}+\zeta_{17}^{-1}+\zeta_{17}^{2}+\zeta_{17}^{-2}+\zeta_{17}^{4}+\zeta_{17}^{-4}+\zeta_{17}^{8}+\zeta_{17}^{-8}$

Published on 25 Mar 2026 - 8:13

score 1k · Answer 6 · 2026-04-16 14:24:39

1k

Views

Algebraic Closure of Finite Field $\mathbb{F}_p$

Published on 16 Apr 2026 - 14:24

score 173 · Answer 7 · 2026-03-29 15:16:47

173

Views

Understanding Automorphism in Galois for Beginners by John Stillwell

Published on 29 Mar 2026 - 15:16

score 73 · Answer 8 · 2026-03-26 08:03:25

73

Views

Elements of a semigroup/ring that are powers of each other

Published on 26 Mar 2026 - 8:03

score 43 · Answer 9 · 2026-04-09 05:31:54

43

Views

How can a field L be a subgroup of the Galois group of the extension L:K?

Published on 09 Apr 2026 - 5:31

score 66 · Answer 10 · 2026-04-11 01:59:26

66

Views

What is the biggest field extension of rational numbers with known equality comparison algorithm?

Published on 11 Apr 2026 - 1:59

score 83 · Answer 11 · 2026-04-02 10:17:46

83

Views

Find $[\mathbb{Q}(14^{1/8}) : \mathbb{Q}(14^{1/2})]$

Published on 02 Apr 2026 - 10:17

score 82 · Answer 12 · 2026-04-26 00:00:28

82

Views

Transcendence of $e(T)$

Published on 26 Apr 2026 - 0:00

score 717 · Answer 13 · 2026-04-15 22:55:05

717

Views

Let $\Phi_n(x)$ denote the cyclotomic polynomial of order $n$. Show that if $n>1$ is odd, then $\Phi_{2n}(x)=\Phi_n(-x)$

Published on 15 Apr 2026 - 22:55

score 586 · Answer 14 · 2026-04-14 05:02:59

586

Views

Which matrices $A\in\text{Mat}_{n\times n}(\mathbb{K})$ are orthogonally diagonalizable over $\mathbb{K}$?

Published on 14 Apr 2026 - 5:02

score 77 · Answer 15 · 2026-04-17 00:39:09

77

Views

Find all ring maps $\mathbb{Q}[x]/(x^{101}+2)\longrightarrow\mathbb{Q}[x]/(x^{501}-2)$

Published on 17 Apr 2026 - 0:39

List Question

Take a galois group $Gal(K/\mathbb{Q})$ isomorphic to $C_{16}$. How many subfields $L$ exist such that $[K:L] = 4$?

Is element in infinitely generated field extension contained in finitely generated field extension?

Minimal polynomial of $\eta_4$ over $\mathbb{Q}(\eta_2)$.

A question regarding the definition of a quadratic field

Evaluate sum roots of unity $\zeta_{17}+\zeta_{17}^{-1}+\zeta_{17}^{2}+\zeta_{17}^{-2}+\zeta_{17}^{4}+\zeta_{17}^{-4}+\zeta_{17}^{8}+\zeta_{17}^{-8}$

Algebraic Closure of Finite Field $\mathbb{F}_p$

Understanding Automorphism in Galois for Beginners by John Stillwell

Elements of a semigroup/ring that are powers of each other

How can a field L be a subgroup of the Galois group of the extension L:K?

What is the biggest field extension of rational numbers with known equality comparison algorithm?

Find $[\mathbb{Q}(14^{1/8}) : \mathbb{Q}(14^{1/2})]$

Transcendence of $e(T)$

Let $\Phi_n(x)$ denote the cyclotomic polynomial of order $n$. Show that if $n>1$ is odd, then $\Phi_{2n}(x)=\Phi_n(-x)$

Which matrices $A\in\text{Mat}_{n\times n}(\mathbb{K})$ are orthogonally diagonalizable over $\mathbb{K}$?

Find all ring maps $\mathbb{Q}[x]/(x^{101}+2)\longrightarrow\mathbb{Q}[x]/(x^{501}-2)$

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