Question

Galois extension of real subfield is of degree at most $2$?

score 251 · Answer 1 · 2014-06-16 05:02:16

251

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Galois extension of real subfield is of degree at most $2$?

Published on 16 Jun 2014 - 5:02

score 4.2k · Answer 2 · 2026-03-25 11:15:02

4.2k

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Is a polynomial equation of degree $\ge 5$ not solvable by any way?

Published on 25 Mar 2026 - 11:15

score 323 · Answer 3 · 2026-03-25 03:07:44

323

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Is there any relation between Galois solvability and integrability of hamiltonian systems?

Published on 25 Mar 2026 - 3:07

score 268 · Answer 4 · 2014-06-16 15:31:13

268

Views

Splitting field of $f$ as smallest field extension containing all BUT ONE zero of $f$

Published on 16 Jun 2014 - 15:31

score 1.8k · Answer 5 · 2014-06-16 17:57:58

1.8k

Views

Polynomial of degree $7$ with cyclic Galois group

Published on 16 Jun 2014 - 17:57

score 246 · Answer 6 · 2026-04-02 02:14:03

246

Views

Does the data of Galois group, ramified places, and inertia groups, determine a Galois number field?

Published on 02 Apr 2026 - 2:14

score 4.3k · Answer 7 · 2014-06-17 01:50:17

4.3k

Views

Proof of Dedekind's Theorem on the Galois Groups of rational polynomials

Published on 17 Jun 2014 - 1:50

score 945 · Answer 8 · 2014-06-17 05:10:32

945

Views

Maximal Subfield of $\mathbb C$ without $\sqrt{2}$

Published on 17 Jun 2014 - 5:10

score 1k · Answer 9 · 2014-06-17 06:48:46

1k

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Does a maximal subfield of $\mathbb C$ not containing $\sqrt{2}$ have index $2$?

Published on 17 Jun 2014 - 6:48

score 74 · Answer 10 · 2014-06-17 17:51:02

74

Views

If $|\operatorname{Aut}_KF|=3$, must we have cube roots of unity?

Published on 17 Jun 2014 - 17:51

score 102 · Answer 11 · 2014-06-17 18:52:51

102

Views

If $K$ is a maximal subfield of $\mathbb C$ without $\sqrt{2}$, does $K\overline{\mathbb Q}=\mathbb C$?

Published on 17 Jun 2014 - 18:52

score 12.7k · Answer 12 · 2014-06-18 00:56:07

12.7k

Views

Proving that a polynomial is not solvable by radicals.

Published on 18 Jun 2014 - 0:56

score 490 · Answer 13 · 2014-06-18 05:55:07

490

Views

Proof Verification/Strategy: Galois Group of the splitting field of a polynomial is solvable.

Published on 18 Jun 2014 - 5:55

score 59 · Answer 14 · 2014-06-18 18:55:20

59

Views

Find polynomials $u(x), v(x)$ satisfying $X^5 + X^2 = (X^3 + X + 1)u(x) + v(x)$

Published on 18 Jun 2014 - 18:55

score 141 · Answer 15 · 2026-04-02 02:07:47

141

Views

Galois extension of two fields

Published on 02 Apr 2026 - 2:07

List Question

Galois extension of real subfield is of degree at most $2$?

Is a polynomial equation of degree $\ge 5$ not solvable by any way?

Is there any relation between Galois solvability and integrability of hamiltonian systems?

Splitting field of $f$ as smallest field extension containing all BUT ONE zero of $f$

Polynomial of degree $7$ with cyclic Galois group

Does the data of Galois group, ramified places, and inertia groups, determine a Galois number field?

Proof of Dedekind's Theorem on the Galois Groups of rational polynomials

Maximal Subfield of $\mathbb C$ without $\sqrt{2}$

Does a maximal subfield of $\mathbb C$ not containing $\sqrt{2}$ have index $2$?

If $|\operatorname{Aut}_KF|=3$, must we have cube roots of unity?

If $K$ is a maximal subfield of $\mathbb C$ without $\sqrt{2}$, does $K\overline{\mathbb Q}=\mathbb C$?

Proving that a polynomial is not solvable by radicals.

Proof Verification/Strategy: Galois Group of the splitting field of a polynomial is solvable.

Find polynomials $u(x), v(x)$ satisfying $X^5 + X^2 = (X^3 + X + 1)u(x) + v(x)$

Galois extension of two fields

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