List questions from galois-theory

Published on 05 Apr 2014 - 13:36

145

Views

Determine $\text{Gal}(\mathbb{Q}(\alpha) / \mathbb{Q})$ where $\alpha = \omega + \omega^7 + \omega^{11}$

Published on 05 Apr 2014 - 13:49

113

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find the number of solutions of the equation $a_1x_1+a_2x_2+...+a_nx_n=0$ in a linear space over Galois field

Published on 30 Mar 2026 - 2:08

555

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What does root of unity in $\mathbb{Z}_p$ look like?

Published on 26 Mar 2026 - 21:35

387

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Understanding the Fundamental Theorem of Galois Theory (Artin's Text)

Published on 07 Apr 2014 - 16:08

374

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The degree of the splitting field of $X^6+X^3+1$

Published on 07 Apr 2014 - 17:21

83

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$p(x) \in F[x]$ Has One Root in Normal Field Extension $E$ $\implies$ $p(x)$ Splits Entirely in $E$

Published on 08 Apr 2014 - 1:46

29

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$F \subset L \subset E$ s.t. $L,E$ Normal $\implies$ Elements of $G(E/F)$ Map $L$ onto itself.

Published on 08 Apr 2014 - 2:06

271

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Roots of Unity: Sums, Products, and Field Extensions

Published on 25 Mar 2026 - 22:10

32

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A Question about Cubic and Galois Fields

Published on 26 Mar 2026 - 1:02

86

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Isomorphism betwixt a Galois Group and the set of $n$th roots of unity

Published on 26 Mar 2026 - 1:23

295

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Galois field of order $p^n$

Published on 30 Mar 2026 - 2:06

989

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Proof Verification of the Primitive Element Theorem

Published on 08 Apr 2014 - 14:06

174

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A question on solvable groups.

Published on 25 Mar 2026 - 9:33

102

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Problem about Galois Extension.

Published on 29 Mar 2026 - 19:25

List Question

Inverse Galois theory and Hilbert class field

Determine $\text{Gal}(\mathbb{Q}(\alpha) / \mathbb{Q})$ where $\alpha = \omega + \omega^7 + \omega^{11}$

find the number of solutions of the equation $a_1x_1+a_2x_2+...+a_nx_n=0$ in a linear space over Galois field

What does root of unity in $\mathbb{Z}_p$ look like?

Understanding the Fundamental Theorem of Galois Theory (Artin's Text)

The degree of the splitting field of $X^6+X^3+1$

$p(x) \in F[x]$ Has One Root in Normal Field Extension $E$ $\implies$ $p(x)$ Splits Entirely in $E$

$F \subset L \subset E$ s.t. $L,E$ Normal $\implies$ Elements of $G(E/F)$ Map $L$ onto itself.

Roots of Unity: Sums, Products, and Field Extensions

A Question about Cubic and Galois Fields

Isomorphism betwixt a Galois Group and the set of $n$th roots of unity

Galois field of order $p^n$

Proof Verification of the Primitive Element Theorem

A question on solvable groups.

Problem about Galois Extension.

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