List questions from galois-theory

Published on 01 Apr 2026 - 20:53

112

Views

Galois group of $K(\sqrt[p]a)$ over $K$

Published on 19 May 2014 - 18:30

252

Views

Field extension, primitive root of unity solvable by radicals

Published on 19 May 2014 - 20:26

59

Views

E is a Galois extension of F

Published on 01 Apr 2026 - 20:49

202

Views

Having trouble considering a finite field $\mathbb{F}_{p^n}$ as a vector space over $\mathbb{F}_p$.

Published on 30 Mar 2026 - 10:40

148

Views

$L=K(\alpha)$ with $\alpha^p-\alpha=a\in K$

Published on 01 Apr 2026 - 20:48

1.4k

Views

Automorphisms of a field extension permute roots of irreducible factors.

Published on 20 May 2014 - 17:46

898

Views

If $\widetilde{L} =$ splitting field of all irreducible polynomials over $L$ of prime-power degree, is $\widetilde{\Bbb{Q}} = \overline{\Bbb{Q}}$?

Published on 21 May 2014 - 3:51

69

Views

M/F normal, determine whether there is an automorphism $\sigma\in Gal(M/F)$ with $\sigma(a)=a'$ and $\sigma(b)=b'$

Published on 21 May 2014 - 21:24

300

Views

Subgroup of class group

Published on 22 May 2014 - 3:36

62

Views

Char(F)=0, K/F is abelian and F contains a primitive root of unity

Published on 29 Mar 2026 - 8:16

1.1k

Views

Splitting field of cyclotomic polynomials over $\mathbb{F}_2$.

Published on 26 Mar 2026 - 4:51

4.7k

Views

Why there is much interest in the study of $\operatorname{Gal}\left(\overline{\mathbb Q}/\mathbb Q\right)$?

Published on 25 Mar 2026 - 0:53

262

Views

Is the extension Galois if $\mathrm{Aut}(K)$ acts transitively on the non-ramified prime ideals?

Published on 22 May 2014 - 8:12

192

Views

When is a number in $\mathbb{Q}(\sqrt{a_1},\ldots,\sqrt{a_n})$?

Published on 26 Mar 2026 - 4:52

List Question

A question about Galois extension

Galois group of $K(\sqrt[p]a)$ over $K$

Field extension, primitive root of unity solvable by radicals

E is a Galois extension of F

Having trouble considering a finite field $\mathbb{F}_{p^n}$ as a vector space over $\mathbb{F}_p$.

$L=K(\alpha)$ with $\alpha^p-\alpha=a\in K$

Automorphisms of a field extension permute roots of irreducible factors.

If $\widetilde{L} =$ splitting field of all irreducible polynomials over $L$ of prime-power degree, is $\widetilde{\Bbb{Q}} = \overline{\Bbb{Q}}$?

M/F normal, determine whether there is an automorphism $\sigma\in Gal(M/F)$ with $\sigma(a)=a'$ and $\sigma(b)=b'$

Subgroup of class group

Char(F)=0, K/F is abelian and F contains a primitive root of unity

Splitting field of cyclotomic polynomials over $\mathbb{F}_2$.

Why there is much interest in the study of $\operatorname{Gal}\left(\overline{\mathbb Q}/\mathbb Q\right)$?

Is the extension Galois if $\mathrm{Aut}(K)$ acts transitively on the non-ramified prime ideals?

When is a number in $\mathbb{Q}(\sqrt{a_1},\ldots,\sqrt{a_n})$?

Trending Questions

Popular # Hahtags

Popular Questions