List questions from galois-theory

Published on 27 May 2014 - 18:46

98

Views

Proving that $\mid Gal(E/F)\mid\leq [E:F]$ by induction

Published on 01 Apr 2026 - 20:48

688

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if $K/F$ is a Galois extension, show that any intermediate field $L$ is generated by the traces of elements from $K$ over $L$.

Published on 28 May 2014 - 2:10

190

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Show $\mathbb{Q}(\zeta)$ does not contain $\sqrt{7}$

Published on 28 May 2014 - 15:10

2.2k

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Help with computing Galois group of $x^4 - 3$.

Published on 29 May 2014 - 5:32

214

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Subgroups of a Galois group $G$

Published on 30 May 2014 - 13:17

1k

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A Galois Extension over a field of characteristic p

Published on 25 Mar 2026 - 14:25

1.1k

Views

Intersection of ideals is zero then $R$ is Noetherian

Published on 25 Mar 2026 - 20:09

291

Views

The Galois group of the finite field's algebraic closure is not countable

Published on 30 Mar 2026 - 12:02

166

Views

Characterisation of Galois Group with the action of $\sigma \in S_n$ on the roots

Published on 25 Mar 2026 - 1:18

3.2k

Views

Find all subfields in extension $\mathbb{Q}\subseteq \mathbb{Q}(\sqrt[4]{2})$

Published on 26 Mar 2026 - 6:25

1.5k

Views

Galois group of $x^4 - 25$.

Published on 01 Jun 2014 - 23:16

3.3k

Views

Galois group of $x^3 + x^2 - 2x - 1$.

Published on 02 Jun 2014 - 0:39

792

Views

Conjugate Groups of Galois Group if and only if Isomorphic Extensions

Published on 02 Jun 2014 - 2:18

573

Views

Extending Automorphisms, Isomorphisms

Published on 01 Apr 2026 - 22:35

List Question

The solution to $x^n = -1$ over finite field.

Proving that $\mid Gal(E/F)\mid\leq [E:F]$ by induction

if $K/F$ is a Galois extension, show that any intermediate field $L$ is generated by the traces of elements from $K$ over $L$.

Show $\mathbb{Q}(\zeta)$ does not contain $\sqrt{7}$

Help with computing Galois group of $x^4 - 3$.

Subgroups of a Galois group $G$

A Galois Extension over a field of characteristic p

Intersection of ideals is zero then $R$ is Noetherian

The Galois group of the finite field's algebraic closure is not countable

Characterisation of Galois Group with the action of $\sigma \in S_n$ on the roots

Find all subfields in extension $\mathbb{Q}\subseteq \mathbb{Q}(\sqrt[4]{2})$

Galois group of $x^4 - 25$.

Galois group of $x^3 + x^2 - 2x - 1$.

Conjugate Groups of Galois Group if and only if Isomorphic Extensions

Extending Automorphisms, Isomorphisms

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