Question

Let $f(x)\in \Bbb{F}_p[x]$ be an irreducible polynomial of degree $m$, what is the number of irreducible factors of $f(x)$ in $\Bbb{F}_{p^n}[x]$?

score 63 · Answer 1 · 2021-09-07 04:35:54

63

Views

Let $f(x)\in \Bbb{F}_p[x]$ be an irreducible polynomial of degree $m$, what is the number of irreducible factors of $f(x)$ in $\Bbb{F}_{p^n}[x]$?

Published on 07 Sep 2021 - 4:35

score 55 · Answer 2 · 2021-09-08 19:52:26

55

Views

Why is a morphism dominating? (In GIT by Mumford)

Published on 08 Sep 2021 - 19:52

score 273 · Answer 3 · 2021-09-08 21:03:16

273

Views

Length of orbits in group actions

Published on 08 Sep 2021 - 21:03

score 252 · Answer 4 · 2026-04-05 17:18:14

252

Views

Quotient space of a circle action on the 5-sphere

Published on 05 Apr 2026 - 17:18

score 27 · Answer 5 · 2026-04-04 10:58:42

27

Views

Showing that two group actions are not equivalent

Published on 04 Apr 2026 - 10:58

score 161 · Answer 6 · 2026-04-07 01:05:25

161

Views

Quotient group of $S^3$ by a cyclic group is always a lens space

Published on 07 Apr 2026 - 1:05

score 228 · Answer 7 · 2026-03-28 03:56:13

228

Views

Reference request: Quotients of $S^3=SU(2)$ by finite subgroups

Published on 28 Mar 2026 - 3:56

score 27 · Answer 8 · 2026-03-29 03:03:36

27

Views

Measures of Rotated Sets in $\mathbb{R}^n$

Published on 29 Mar 2026 - 3:03

score 142 · Answer 9 · 2021-09-17 00:19:41

142

Views

Stabilizers: If $X$ is a $G$-set and $x, y \in X$ such that $y=hx$ for some $h\in G$, show that $G_x$ and $G_y$ are isomorphic

Published on 17 Sep 2021 - 0:19

score 284 · Answer 10 · 2021-09-17 22:06:13

284

Views

Suppose $G$ is a abelian, transitive subgroup of $S_n$. Prove that for all $x\in\{1,\dots,n\}$, $G_x=\langle 1\rangle$

Published on 17 Sep 2021 - 22:06

score 38 · Answer 11 · 2026-03-29 08:20:54

38

Views

Understanding why we need "mod n" in the definition of $r(j)$?

Published on 29 Mar 2026 - 8:20

score 73 · Answer 12 · 2026-03-29 08:20:54

73

Views

Why the action of $D_{2n}$ on $\{a_i\}$ should look like this?

Published on 29 Mar 2026 - 8:20

score 73 · Answer 13 · 2021-09-20 08:09:19

73

Views

Showing that two elements of a group have no relations between them using group actions

Published on 20 Sep 2021 - 8:09

score 57 · Answer 14 · 2026-03-26 04:34:59

57

Views

Let $V$ be a finite vector space over $K$ and $X:=\{\bar{x}=(x_1,\ldots,x_{n+1})\in V^{n+1} : (x_1,\ldots,x_{n})\in \mathcal{B}$. Then…

Published on 26 Mar 2026 - 4:34

score 43 · Answer 15 · 2021-09-21 10:33:03

43

Views

Lie group actions induces a manifold structure

Published on 21 Sep 2021 - 10:33

List Question

Let $f(x)\in \Bbb{F}_p[x]$ be an irreducible polynomial of degree $m$, what is the number of irreducible factors of $f(x)$ in $\Bbb{F}_{p^n}[x]$?

Why is a morphism dominating? (In GIT by Mumford)

Length of orbits in group actions

Quotient space of a circle action on the 5-sphere

Showing that two group actions are not equivalent

Quotient group of $S^3$ by a cyclic group is always a lens space

Reference request: Quotients of $S^3=SU(2)$ by finite subgroups

Measures of Rotated Sets in $\mathbb{R}^n$

Stabilizers: If $X$ is a $G$-set and $x, y \in X$ such that $y=hx$ for some $h\in G$, show that $G_x$ and $G_y$ are isomorphic

Suppose $G$ is a abelian, transitive subgroup of $S_n$. Prove that for all $x\in\{1,\dots,n\}$, $G_x=\langle 1\rangle$

Understanding why we need "mod n" in the definition of $r(j)$?

Why the action of $D_{2n}$ on $\{a_i\}$ should look like this?

Showing that two elements of a group have no relations between them using group actions

Let $V$ be a finite vector space over $K$ and $X:=\{\bar{x}=(x_1,\ldots,x_{n+1})\in V^{n+1} : (x_1,\ldots,x_{n})\in \mathcal{B}$. Then…

Lie group actions induces a manifold structure

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