List questions from galois-extensions

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Non-galois real extensions of $\mathbb Q$

Published on 22 Mar 2026 - 16:09

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How is $\operatorname{Gal}(K^{nr}/K)$ isomorphic to $\operatorname{Gal}(\bar{k}/k)$?

Published on 20 Mar 2026 - 7:00

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Corollary of Proposition 11 in Lang's Algebraic Number Theory

Published on 20 Mar 2026 - 4:19

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The automorphisms of the extension $\mathbb{Q}(\sqrt[4]{2})/\mathbb{Q}$.

Published on 22 Mar 2026 - 4:25

276

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First cohomology group of the $n$-torsion of an elliptic curve

Published on 20 Mar 2026 - 12:27

90

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Given a Galois extension with $Gal_F(E) \simeq S_3$, is $E$ a splitting field of an irreducible cubic polynomial over F?

Published on 20 Mar 2026 - 6:11

123

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Polynomial coefficients from GF(2^k) to GF(2)

Published on 21 Mar 2026 - 16:09

72

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$\mathbb{Q}(t+t^{-1}) \subseteq \mathbb{Q}(t)$, where $t$ is a variable

Published on 22 Mar 2026 - 13:47

549

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Is the integral closure of a ring of integers in finite separable extension a ring of integers?

Published on 24 Mar 2026 - 10:55

100

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If $S<G:=\text{Gal}(E/R)$ is a Sylow 2-subgroup, then $[\text{Fix}_E(S):R] = [G:S]$

Published on 20 Mar 2026 - 10:44

466

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Given a galois group find the polynomial

Published on 25 Mar 2026 - 14:56

140

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Find a splitting field for $f(x) = x^6 − 2 $ over $GF(7)$ .

Published on 25 Mar 2026 - 9:49

503

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Galois extension from $GF(5)$ to $GF(25)$.

Published on 25 Mar 2026 - 20:52

180

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Jacobi form to Weierstrass form . . . lattices included .... polynomial factoring in the way

Published on 22 Mar 2026 - 10:44

List Question

Fixed points of automorphisms of $\mathbb{Q}(\zeta)$

Non-galois real extensions of $\mathbb Q$

How is $\operatorname{Gal}(K^{nr}/K)$ isomorphic to $\operatorname{Gal}(\bar{k}/k)$?

Corollary of Proposition 11 in Lang's Algebraic Number Theory

The automorphisms of the extension $\mathbb{Q}(\sqrt[4]{2})/\mathbb{Q}$.

First cohomology group of the $n$-torsion of an elliptic curve

Given a Galois extension with $Gal_F(E) \simeq S_3$, is $E$ a splitting field of an irreducible cubic polynomial over F?

Polynomial coefficients from GF(2^k) to GF(2)

$\mathbb{Q}(t+t^{-1}) \subseteq \mathbb{Q}(t)$, where $t$ is a variable

Is the integral closure of a ring of integers in finite separable extension a ring of integers?

If $S<G:=\text{Gal}(E/R)$ is a Sylow 2-subgroup, then $[\text{Fix}_E(S):R] = [G:S]$

Given a galois group find the polynomial

Find a splitting field for $f(x) = x^6 − 2 $ over $GF(7)$ .

Galois extension from $GF(5)$ to $GF(25)$.

Jacobi form to Weierstrass form . . . lattices included .... polynomial factoring in the way

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