List questions from galois-theory

Published on 25 Mar 2026 - 14:39

47

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Interpretation of Abelian Extension?

Published on 27 Mar 2026 - 11:46

191

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Galois group of the polynomial $(x^p-a)(x^q-a)$.

Published on 15 Jul 2018 - 13:27

219

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Minimal polynomial for $\sqrt[5]{2}$ over $\mathbb Q(\sqrt[]{3})$

Published on 25 Mar 2026 - 14:32

131

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How can we "discover" the Vandermonde polynomial?

Published on 15 Jul 2018 - 20:47

27

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What is the significance of considering characteristic $p$ dividing $n(n-1)$, in finding the Galois group of a equation of degree $n$

Published on 16 Jul 2018 - 4:05

1k

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Confusion about the splitting field of $x^3-7$

Published on 25 Mar 2026 - 14:47

984

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Prove that the Galois group of an irreducible cubic polynomial over $\mathbb{Q}$ is isomorphic to $S_3$ or $\mathbb{Z}_3$

Published on 16 Jul 2018 - 23:40

176

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$\mathbb{Q}[\sqrt{2},\sqrt{3},\dots,\sqrt{n}]=\mathbb{Q}[\sqrt{2}+\sqrt{3}+\cdots+\sqrt{n}]$

Published on 17 Jul 2018 - 10:51

193

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$x^4+x+1 \in\mathbb{Z}_2[x]$ - Galois group

Published on 25 Mar 2026 - 14:39

442

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Test of irreducibility of a binary polynomial

Published on 25 Mar 2026 - 14:37

178

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Prove that $K$ and $L$ are conjugate iff $G(E/K)$ and $G(E/L)$ are conjugate subgroups of $G(E/F)$

Published on 18 Jul 2018 - 16:48

96

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$|Gal(f(x),\mathbb Q )|$?

Published on 27 Mar 2026 - 14:58

35

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Let $K⊆M⊆L$, such that $[L:K]=n$ for some $n∈\mathbb{N}$. Prove $[M:K]$ is well-defined.

Published on 19 Jul 2018 - 20:29

980

Views

Express the inertia group in terms of the maximal unramified extension

Published on 23 Jul 2018 - 12:50

List Question

Galois group is isomorphic to $S_5$?

Interpretation of Abelian Extension?

Galois group of the polynomial $(x^p-a)(x^q-a)$.

Minimal polynomial for $\sqrt[5]{2}$ over $\mathbb Q(\sqrt[]{3})$

How can we "discover" the Vandermonde polynomial?

What is the significance of considering characteristic $p$ dividing $n(n-1)$, in finding the Galois group of a equation of degree $n$

Confusion about the splitting field of $x^3-7$

Prove that the Galois group of an irreducible cubic polynomial over $\mathbb{Q}$ is isomorphic to $S_3$ or $\mathbb{Z}_3$

$\mathbb{Q}[\sqrt{2},\sqrt{3},\dots,\sqrt{n}]=\mathbb{Q}[\sqrt{2}+\sqrt{3}+\cdots+\sqrt{n}]$

$x^4+x+1 \in\mathbb{Z}_2[x]$ - Galois group

Test of irreducibility of a binary polynomial

Prove that $K$ and $L$ are conjugate iff $G(E/K)$ and $G(E/L)$ are conjugate subgroups of $G(E/F)$

$|Gal(f(x),\mathbb Q )|$?

Let $K⊆M⊆L$, such that $[L:K]=n$ for some $n∈\mathbb{N}$. Prove $[M:K]$ is well-defined.

Express the inertia group in terms of the maximal unramified extension

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