List questions from galois-extensions

Published on 13 Apr 2026 - 7:24

125

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Galois Group of $x^2-25$ over $\mathbb{Q}$

Published on 14 Apr 2026 - 3:07

359

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Showing that the Galois group has an element of order 8.

Published on 10 May 2026 - 17:16

993

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Galois group of $x^3-3x-1$ over $\mathbb{Q}$

Published on 15 Apr 2026 - 14:12

387

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Is : $ \mathrm{Gal} \ : \ F/ \mathbb{Q} \to \mathrm{Gal} (F / \mathbb{Q} ) $ represented by $ \overline{ \mathbb{Q} } $?

Published on 14 May 2026 - 6:15

322

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Inverse Galois problem

Published on 14 May 2026 - 3:56

198

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Show that $ \operatorname{Gal}(\mathbb{Q}(\sqrt[4]{2}\,)/\mathbb{Q}) \simeq \mathbb{Z}_{4}$, or prove otherwise

Published on 15 Apr 2026 - 18:34

1.4k

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Does a field extension $L$ of $F$ have the same characteristic as $F$?

Published on 14 Apr 2026 - 10:31

115

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Decrease in algebraic degree on multiplying a real number with a root of unity

Published on 14 May 2026 - 7:38

1.1k

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Existence of Galois Closure

Published on 11 Apr 2026 - 17:40

320

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Galois Closure and a natural bijection

Published on 11 Apr 2026 - 17:59

57

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If $L/K$ is algebraic, is $L$ a subfield of some algebraic closure $\bar K$ of $K$?

Published on 14 Apr 2026 - 13:28

1.1k

Views

Show a regular n-sided polygon is constructible, using only ruler and compasses, iff the number $\alpha = 2 \cos(2\pi/n)$ is constructible.

Published on 11 May 2026 - 1:48

332

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Inertia coprime to degree implies Inertia cyclic?

Published on 10 May 2026 - 14:06

655

Views

To prove any real Galois extension of $\mathbb{Q}$ of odd degree must not be radical

Published on 16 Apr 2026 - 8:36

List Question

Galois group in $\mathbb{C}$

Galois Group of $x^2-25$ over $\mathbb{Q}$

Showing that the Galois group has an element of order 8.

Galois group of $x^3-3x-1$ over $\mathbb{Q}$

Is : $ \mathrm{Gal} \ : \ F/ \mathbb{Q} \to \mathrm{Gal} (F / \mathbb{Q} ) $ represented by $ \overline{ \mathbb{Q} } $?

Inverse Galois problem

Show that $ \operatorname{Gal}(\mathbb{Q}(\sqrt[4]{2}\,)/\mathbb{Q}) \simeq \mathbb{Z}_{4}$, or prove otherwise

Does a field extension $L$ of $F$ have the same characteristic as $F$?

Decrease in algebraic degree on multiplying a real number with a root of unity

Existence of Galois Closure

Galois Closure and a natural bijection

If $L/K$ is algebraic, is $L$ a subfield of some algebraic closure $\bar K$ of $K$?

Show a regular n-sided polygon is constructible, using only ruler and compasses, iff the number $\alpha = 2 \cos(2\pi/n)$ is constructible.

Inertia coprime to degree implies Inertia cyclic?

To prove any real Galois extension of $\mathbb{Q}$ of odd degree must not be radical

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