Question

Why p-cyclic extension iff $p^m$-cyclic extension $\forall m$

score 114 · Answer 1 · 2026-03-23 04:26:55

114

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Why p-cyclic extension iff $p^m$-cyclic extension $\forall m$

Published on 23 Mar 2026 - 4:26

score 536 · Answer 2 · 2026-03-27 02:07:08

536

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Is there any degree 6 irreducible polynomial in $\Bbb Q[x]$ whose Galois group is $A_4$?

Published on 27 Mar 2026 - 2:07

score 139 · Answer 3 · 2019-05-26 15:41:37

$\omega$ is the $11$th primitive root of unity. Find minimal polynomial of $\beta=\omega+\omega^3+\omega^4+\omega^5+\omega^9$

score 155 · Answer 4 · 2019-05-26 18:42:06

155

Views

Galois group of $(x^3-2)(x^5-1)$ over $\mathbb{Q}$.

Published on 26 May 2019 - 18:42

score 124 · Answer 5 · 2019-05-27 08:01:18

124

Views

About the reduction modulo $p$ for calculating Galois groups

Published on 27 May 2019 - 8:01

score 110 · Answer 6 · 2026-03-28 06:40:36

110

Views

$p$'th roots in an extension of prime degree $p$.

Published on 28 Mar 2026 - 6:40

score 264 · Answer 7 · 2026-03-26 22:57:58

264

Views

Example of exotic $S_5$ as a Galois group

Published on 26 Mar 2026 - 22:57

score 178 · Answer 8 · 2026-03-26 04:32:01

178

Views

Finding subfields with Galois group of order 20

Published on 26 Mar 2026 - 4:32

score 155 · Answer 9 · 2026-03-31 22:08:06

155

Views

Can the number of isomorphisms be less than the degree of field extension?

Published on 31 Mar 2026 - 22:08

score 221 · Answer 10 · 2019-05-31 00:05:42

221

Views

How do I find the roots of an iterated polynomial which is "solvable".

Published on 31 May 2019 - 0:05

score 124 · Answer 11 · 2026-03-31 22:06:42

124

Views

Determine the Degree extension of $K$ over $\mathbb{Q}$

Published on 31 Mar 2026 - 22:06

score 243 · Answer 12 · 2019-05-31 09:54:20

243

Views

Extension of scalars of an irreducible representation - Is it a direct sum over a single orbit of Galois conjugates?

Published on 31 May 2019 - 9:54

score 303 · Answer 13 · 2026-03-25 23:52:30

303

Views

Galois group of $x^6+1$ over $\mathbb{F}_2$

Published on 25 Mar 2026 - 23:52

score 48 · Answer 14 · 2026-03-29 07:19:46

48

Views

Is $\mathbb{F}_p(X)/\mathbb{F}_p(X^2)$ Galois extension?

Published on 29 Mar 2026 - 7:19

score 49 · Answer 15 · 2019-05-31 17:23:46

49

Views

Given a quadratic extension $K/F$, is there a quadratic extension $L/K$ such that $ \operatorname{Gal}(L'/F)=D_4$

Published on 31 May 2019 - 17:23

List Question

Why p-cyclic extension iff $p^m$-cyclic extension $\forall m$

Is there any degree 6 irreducible polynomial in $\Bbb Q[x]$ whose Galois group is $A_4$?

$\omega$ is the $11$th primitive root of unity. Find minimal polynomial of $\beta=\omega+\omega^3+\omega^4+\omega^5+\omega^9$

Galois group of $(x^3-2)(x^5-1)$ over $\mathbb{Q}$.

About the reduction modulo $p$ for calculating Galois groups

$p$'th roots in an extension of prime degree $p$.

Example of exotic $S_5$ as a Galois group

Finding subfields with Galois group of order 20

Can the number of isomorphisms be less than the degree of field extension?

How do I find the roots of an iterated polynomial which is "solvable".

Determine the Degree extension of $K$ over $\mathbb{Q}$

Extension of scalars of an irreducible representation - Is it a direct sum over a single orbit of Galois conjugates?

Galois group of $x^6+1$ over $\mathbb{F}_2$

Is $\mathbb{F}_p(X)/\mathbb{F}_p(X^2)$ Galois extension?

Given a quadratic extension $K/F$, is there a quadratic extension $L/K$ such that $ \operatorname{Gal}(L'/F)=D_4$

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