List questions from galois-extensions

Published on 30 Apr 2022 - 3:56

59

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Degrees of field extensions

Published on 02 May 2022 - 6:35

129

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Compositum of intersection fields

Published on 05 May 2022 - 3:01

118

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Infinitely large Galois extensions of $\mathbb Q$ inside $\mathbb Q_p$

Published on 11 May 2022 - 12:08

62

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Is $i$ an element of $\mathbb{Q}(\sqrt[4]{5},w)$ where $w=e^{2πi/3}$?

Published on 12 May 2022 - 12:48

294

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Any element of K(X) which is not in K is transcendental over K

Published on 23 May 2022 - 18:50

53

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Proof verification: given a field $k$, any finite group can be represented as $\rm Gal(E/F)$ where $k\subset F\subset E$ and $E/F$ is Galois.

Published on 25 May 2022 - 9:35

121

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Good reference for Galois theory.

Published on 27 May 2022 - 13:20

179

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Non-normal extension of Q

Published on 23 Feb 2026 - 8:28

109

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The Weil group and maximal tame extension

Published on 25 Mar 2026 - 9:53

62

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Difference in field extensions when the field has $p$ roots of unity versus $p^2$ roots of unity.

Published on 25 Mar 2026 - 16:39

85

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Fundamental Thm of Galois Theory: Showing that $L^H$ is normal over $F$ iff $H$ is normal in $G$

Published on 13 Jun 2022 - 19:08

101

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Galois groups of towers

Published on 14 Jun 2022 - 21:15

105

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Is the extension $\mathbb{Q}(\sqrt{7+\sqrt{7}})/\mathbb{Q}$ a Galois extension?

Published on 23 Feb 2026 - 8:24

63

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Sub-fields of $\mathbb{Q}(a)$ ,$a=\sqrt{4+\sqrt{15}}$ using Galois theory.

Published on 17 Jun 2022 - 17:17

List Question

Tensor product of finite Galois extensions

Degrees of field extensions

Compositum of intersection fields

Infinitely large Galois extensions of $\mathbb Q$ inside $\mathbb Q_p$

Is $i$ an element of $\mathbb{Q}(\sqrt[4]{5},w)$ where $w=e^{2πi/3}$?

Any element of K(X) which is not in K is transcendental over K

Proof verification: given a field $k$, any finite group can be represented as $\rm Gal(E/F)$ where $k\subset F\subset E$ and $E/F$ is Galois.

Good reference for Galois theory.

Non-normal extension of Q

The Weil group and maximal tame extension

Difference in field extensions when the field has $p$ roots of unity versus $p^2$ roots of unity.

Fundamental Thm of Galois Theory: Showing that $L^H$ is normal over $F$ iff $H$ is normal in $G$

Galois groups of towers

Is the extension $\mathbb{Q}(\sqrt{7+\sqrt{7}})/\mathbb{Q}$ a Galois extension?

Sub-fields of $\mathbb{Q}(a)$ ,$a=\sqrt{4+\sqrt{15}}$ using Galois theory.

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