List questions from galois-theory

Published on 28 Mar 2026 - 0:56

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Order of Galois group of $X^n-a$ over $\mathbb{Q}$

Published on 09 Jan 2019 - 22:32

104

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Finding the fields between $\mathbb{Q}(\sqrt{3+\sqrt{7}},\sqrt{3-\sqrt{7}})$ and $\mathbb{Q}$

Published on 30 Mar 2026 - 9:41

266

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What is the minimal polynomial of $\sqrt{3+4i}+\sqrt{3-4i}$ over $\mathbb{Q}$?

Published on 11 Jan 2019 - 18:33

37

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Finding the Galois group of $\mathbb{Q}(2^{1/p},\zeta_{2n})$

Published on 12 Jan 2019 - 4:18

1.3k

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Primitive polynomial of a Galois field

Published on 27 Mar 2026 - 23:20

864

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Irreducible factors of $x^8 - x$ in $Z/2Z[x]$

Published on 27 Mar 2026 - 23:14

195

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Is this a counterexample?

Published on 26 Mar 2026 - 22:58

65

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Noether Equation on Artin and Milgram Galois Theory book

Published on 25 Mar 2026 - 10:57

232

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Does there exist an automorphism of $\mathbb{C}$ that does not keep $\mathbb{R}$ fixed?

Published on 25 Mar 2026 - 18:47

158

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Any Sub-extension of a Radical Extension is Solvable?

Published on 27 Mar 2026 - 18:09

131

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$f(X):= X^n- x\in K[X]$ is irreducible and $Gal(K(y)/K)\cong \mathbb{Z}/n\mathbb{Z}$ if $y$ is a root of $f$

Published on 26 Mar 2026 - 10:43

1.9k

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f irreducible polynomial with $p-2$ real roots $\Rightarrow$ $Gal(\mathbb{Q}_{f}/\mathbb{Q}) \cong S_{p}$

Published on 26 Mar 2026 - 11:01

69

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Can we have two different polynomials of the same degree $d$ here in the factorisation of $x^{p^n} -x$?

Published on 27 Mar 2026 - 18:09

24

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$G \neq gal(E:E_G)$?

Published on 17 Jan 2019 - 14:08

List Question

Compute the Galois group of L over K

Order of Galois group of $X^n-a$ over $\mathbb{Q}$

Finding the fields between $\mathbb{Q}(\sqrt{3+\sqrt{7}},\sqrt{3-\sqrt{7}})$ and $\mathbb{Q}$

What is the minimal polynomial of $\sqrt{3+4i}+\sqrt{3-4i}$ over $\mathbb{Q}$?

Finding the Galois group of $\mathbb{Q}(2^{1/p},\zeta_{2n})$

Primitive polynomial of a Galois field

Irreducible factors of $x^8 - x$ in $Z/2Z[x]$

Is this a counterexample?

Noether Equation on Artin and Milgram Galois Theory book

Does there exist an automorphism of $\mathbb{C}$ that does not keep $\mathbb{R}$ fixed?

Any Sub-extension of a Radical Extension is Solvable?

$f(X):= X^n- x\in K[X]$ is irreducible and $Gal(K(y)/K)\cong \mathbb{Z}/n\mathbb{Z}$ if $y$ is a root of $f$

f irreducible polynomial with $p-2$ real roots $\Rightarrow$ $Gal(\mathbb{Q}_{f}/\mathbb{Q}) \cong S_{p}$

Can we have two different polynomials of the same degree $d$ here in the factorisation of $x^{p^n} -x$?

$G \neq gal(E:E_G)$?

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