Question

A question about how Galois group acts on elements in the extension.

score 139 · Answer 1 · 2018-05-03 04:26:45

139

Views

A question about how Galois group acts on elements in the extension.

Published on 03 May 2018 - 4:26

score 119 · Answer 2 · 2026-03-25 18:54:51

119

Views

Searching for intermediate fields with the Galois correspondence

Published on 25 Mar 2026 - 18:54

score 314 · Answer 3 · 2026-03-22 10:16:16

314

Views

Find Trace and Norm for $K(\alpha)/K$

Published on 22 Mar 2026 - 10:16

score 867 · Answer 4 · 2018-05-05 03:30:27

867

Views

Extension of $\mathbb{Q}[\sqrt{-23}]$ by root of $x^3-x+1$ is Galois

Published on 05 May 2018 - 3:30

score 219 · Answer 5 · 2026-03-25 01:16:58

219

Views

Galois groups and groups of Dirichlet characters

Published on 25 Mar 2026 - 1:16

score 624 · Answer 6 · 2018-05-07 22:22:13

624

Views

Clarification on proof that $\mathbb Q (\zeta _ m) \cap \mathbb Q(\zeta_n) = \mathbb Q$ when $\gcd(m,n) = 1$

Published on 07 May 2018 - 22:22

score 562 · Answer 7 · 2018-05-08 11:18:41

562

Views

Show Galois group of $f(t) = t^5 - 3$ over $\mathbb Q$ is solvable

Published on 08 May 2018 - 11:18

score 230 · Answer 8 · 2018-05-08 15:56:05

230

Views

A field such that no extension has an 11th primitive root of unity

Published on 08 May 2018 - 15:56

score 35 · Answer 9 · 2026-03-26 06:32:31

35

Views

Let $r$ and $n$ be integers. Give the Galois correspondance for the extension $F_{p^r} \cap F_{p^n} \leq F_{p^r} \vee F_{p^n}$

Published on 26 Mar 2026 - 6:32

score 49 · Answer 10 · 2026-03-25 20:22:58

49

Views

Suppose that $f(x)$ has a nonreal root. Show that 2 divides $|\operatorname{Gal}(f(x))|$

Published on 25 Mar 2026 - 20:22

score 159 · Answer 11 · 2026-03-22 12:17:35

159

Views

Constructible $2^{2n + 2}$-th roots of unity

Published on 22 Mar 2026 - 12:17

score 723 · Answer 12 · 2026-03-25 13:55:37

723

Views

Abstract properties of the absolute Galois group over $\mathbb{Q}$

Published on 25 Mar 2026 - 13:55

score 309 · Answer 13 · 2026-03-22 14:10:27

309

Views

Finite extension with abelian Galois group

Published on 22 Mar 2026 - 14:10

score 468 · Answer 14 · 2026-03-25 21:51:11

468

Views

Show that $K$ can be generated over $F$ by the root of an irreducible quartic polynomial of the form $x^4+bx^2+c$.

Published on 25 Mar 2026 - 21:51

score 142 · Answer 15 · 2018-05-16 20:15:26

142

Views

$K=F_3(t)$ show that for every root $\alpha$ of the polynomial $f(x)=x^6-tx^3+1$, $K(\alpha)/K$ is a splliting field

Published on 16 May 2018 - 20:15

List Question

A question about how Galois group acts on elements in the extension.

Searching for intermediate fields with the Galois correspondence

Find Trace and Norm for $K(\alpha)/K$

Extension of $\mathbb{Q}[\sqrt{-23}]$ by root of $x^3-x+1$ is Galois

Galois groups and groups of Dirichlet characters

Clarification on proof that $\mathbb Q (\zeta _ m) \cap \mathbb Q(\zeta_n) = \mathbb Q$ when $\gcd(m,n) = 1$

Show Galois group of $f(t) = t^5 - 3$ over $\mathbb Q$ is solvable

A field such that no extension has an 11th primitive root of unity

Let $r$ and $n$ be integers. Give the Galois correspondance for the extension $F_{p^r} \cap F_{p^n} \leq F_{p^r} \vee F_{p^n}$

Suppose that $f(x)$ has a nonreal root. Show that 2 divides $|\operatorname{Gal}(f(x))|$

Constructible $2^{2n + 2}$-th roots of unity

Abstract properties of the absolute Galois group over $\mathbb{Q}$

Finite extension with abelian Galois group

Show that $K$ can be generated over $F$ by the root of an irreducible quartic polynomial of the form $x^4+bx^2+c$.

$K=F_3(t)$ show that for every root $\alpha$ of the polynomial $f(x)=x^6-tx^3+1$, $K(\alpha)/K$ is a splliting field

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