Question

Proving that the Galois group of the cyclotomic field $\mathbb{Q}(\zeta_n)$ is isomorphic to $U(\mathbb{Z}/n\mathbb{Z})$

score 41 · Answer 1 · 2026-03-25 03:22:14

41

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Proving that the Galois group of the cyclotomic field $\mathbb{Q}(\zeta_n)$ is isomorphic to $U(\mathbb{Z}/n\mathbb{Z})$

Published on 25 Mar 2026 - 3:22

score 3.3k · Answer 2 · 2026-03-25 03:01:19

3.3k

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Krull Topology on Galois Groups (two equivalent(?) definitions).

Published on 25 Mar 2026 - 3:01

score 689 · Answer 3 · 2026-03-28 01:02:52

689

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This matrix is diagonalizable over algebraic closure of $\Bbb F_p$ iff $(n,p)=1$

Published on 28 Mar 2026 - 1:02

score 1.2k · Answer 4 · 2026-03-28 01:02:54

1.2k

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Are all Galois extensions simple?

Published on 28 Mar 2026 - 1:02

score 437 · Answer 5 · 2026-03-28 21:34:27

437

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Galois group of $F_{p^2}$ over $\mathbb{Z}_p$

Published on 28 Mar 2026 - 21:34

score 186 · Answer 6 · 2026-03-26 01:09:29

186

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Symmetric Rational Functions vs Symmetric Polynomials

Published on 26 Mar 2026 - 1:09

score 53 · Answer 7 · 2026-03-29 02:17:09

53

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Help understanding the question

Published on 29 Mar 2026 - 2:17

score 439 · Answer 8 · 2026-03-26 21:10:33

439

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Which subfields of the Galois group of $x^4+8x^2+8x+4$ are Galois and find the splitting field polynomial

Published on 26 Mar 2026 - 21:10

score 173 · Answer 9 · 2026-03-27 22:19:20

173

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Prove that $E=\Bbb Q(\sqrt[d]{a})$

Published on 27 Mar 2026 - 22:19

score 233 · Answer 10 · 2026-03-28 01:02:53

233

Views

Prove that complex conjugation of $\mathbb{C}$ preserves the splitting field

Published on 28 Mar 2026 - 1:02

score 208 · Answer 11 · 2026-02-23 02:53:46

208

Views

A special inverse Galois problem

Published on 23 Feb 2026 - 2:53

score 367 · Answer 12 · 2019-05-01 09:32:07

367

Views

An automorphism in Galois group must map imaginary root to itself or conjugate pair.

Published on 01 May 2019 - 9:32

score 283 · Answer 13 · 2019-05-02 00:45:46

283

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other roots of a minimal polynomial

Published on 02 May 2019 - 0:45

score 436 · Answer 14 · 2019-05-02 13:44:01

436

Views

Algebraic Closure & Algebraic Elements

Published on 02 May 2019 - 13:44

score 297 · Answer 15 · 2026-03-25 03:22:13

297

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Finding minimal polynomial of generator of quadratic subfield of cyclotomic extension $\mathbb{Q}(\xi_{17})$

Published on 25 Mar 2026 - 3:22

List Question

Proving that the Galois group of the cyclotomic field $\mathbb{Q}(\zeta_n)$ is isomorphic to $U(\mathbb{Z}/n\mathbb{Z})$

Krull Topology on Galois Groups (two equivalent(?) definitions).

This matrix is diagonalizable over algebraic closure of $\Bbb F_p$ iff $(n,p)=1$

Are all Galois extensions simple?

Galois group of $F_{p^2}$ over $\mathbb{Z}_p$

Symmetric Rational Functions vs Symmetric Polynomials

Help understanding the question

Which subfields of the Galois group of $x^4+8x^2+8x+4$ are Galois and find the splitting field polynomial

Prove that $E=\Bbb Q(\sqrt[d]{a})$

Prove that complex conjugation of $\mathbb{C}$ preserves the splitting field

A special inverse Galois problem

An automorphism in Galois group must map imaginary root to itself or conjugate pair.

other roots of a minimal polynomial

Algebraic Closure & Algebraic Elements

Finding minimal polynomial of generator of quadratic subfield of cyclotomic extension $\mathbb{Q}(\xi_{17})$

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