Question

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

score 142 · Answer 1 · 2026-04-11 19:10:15

142

Views

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

Published on 11 Apr 2026 - 19:10

score 121 · Answer 2 · 2026-04-15 18:25:52

121

Views

Searching for intermediate fields with the Galois correspondence

Published on 15 Apr 2026 - 18:25

score 317 · Answer 3 · 2026-04-13 09:48:22

317

Views

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

Published on 13 Apr 2026 - 9:48

score 870 · Answer 4 · 2026-04-16 12:57:35

870

Views

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

Published on 16 Apr 2026 - 12:57

score 222 · Answer 5 · 2026-05-10 13:25:08

222

Views

Galois groups and groups of Dirichlet characters

Published on 10 May 2026 - 13:25

score 627 · Answer 6 · 2026-04-15 20:30:18

627

Views

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

Published on 15 Apr 2026 - 20:30

score 565 · Answer 7 · 2026-04-15 04:09:32

565

Views

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

Published on 15 Apr 2026 - 4:09

score 233 · Answer 8 · 2026-04-11 13:15:26

233

Views

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

Published on 11 Apr 2026 - 13:15

score 37 · Answer 9 · 2026-04-17 05:10:57

37

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 17 Apr 2026 - 5:10

score 51 · Answer 10 · 2026-04-16 05:30:00

51

Views

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

Published on 16 Apr 2026 - 5:30

score 162 · Answer 11 · 2026-04-15 21:22:54

162

Views

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

Published on 15 Apr 2026 - 21:22

score 726 · Answer 12 · 2026-05-11 07:50:17

726

Views

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

Published on 11 May 2026 - 7:50

score 312 · Answer 13 · 2026-04-10 12:39:45

312

Views

Finite extension with abelian Galois group

Published on 10 Apr 2026 - 12:39

score 470 · Answer 14 · 2026-04-16 12:43:34

470

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 16 Apr 2026 - 12:43

score 145 · Answer 15 · 2026-04-16 22:26:30

145

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 Apr 2026 - 22:26

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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