List questions from group-actions

Published on 05 Apr 2026 - 21:42

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Generalizing level sets to symplectic actions

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Why must the weak star limit of these counting measures be $SL(2,\mathbb{Z})$ invariant?

Published on 03 Sep 2022 - 0:29

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X admits a fundamental domain iff its orbits are finite

Published on 03 Apr 2026 - 6:05

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Let $G$ be a finite group with a transitive action on $X,|X|=n$. Prove $\forall x,y\in X\exists g\in G$ s.t. $g^{-1}{\rm Stab}_G(x)g={\rm Stab}_G(y)$

Published on 03 Sep 2022 - 15:07

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Let $G$ be a finite abelian group with a transitive faithful action on set $X,|X|=n$. Prove $|G|=n.$

Published on 04 Sep 2022 - 10:12

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$G$ acts transitively on a set $X$, where $|X|=m\in\mathbb{Z}_{>0}$, if and only if there exsits $H\leq G$ with index $m$.

Published on 11 Apr 2026 - 7:39

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What is this space homeomorphic to?

Published on 06 Sep 2022 - 8:02

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Prove that ${\rm Ker}f=\bigcap_{x\in G} xHx^{-1}$, where $H$ is a subgroup of the group $G$, and $f:G\to \text{Sym}(G/H)$ is the left-coset action.

Published on 06 Sep 2022 - 23:13

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Free action of a finite group gives a covering space

Published on 07 Sep 2022 - 10:47

129

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Why is $(12)(34).3 = 4?$

Published on 07 Sep 2022 - 11:05

73

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Name for subgroup of elements commuting with another group action

Published on 07 Sep 2022 - 19:35

104

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Division structure of a torsor

Published on 07 Apr 2026 - 20:55

103

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Reference Request: Groups acting on a topos

Published on 09 Apr 2026 - 15:41

157

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Problem $3E.1$ from Isaacs's "Finite group theory".

Published on 11 Apr 2026 - 10:28

List Question

Determine if this is a left group action

Generalizing level sets to symplectic actions

Why must the weak star limit of these counting measures be $SL(2,\mathbb{Z})$ invariant?

X admits a fundamental domain iff its orbits are finite

Let $G$ be a finite group with a transitive action on $X,|X|=n$. Prove $\forall x,y\in X\exists g\in G$ s.t. $g^{-1}{\rm Stab}_G(x)g={\rm Stab}_G(y)$

Let $G$ be a finite abelian group with a transitive faithful action on set $X,|X|=n$. Prove $|G|=n.$

$G$ acts transitively on a set $X$, where $|X|=m\in\mathbb{Z}_{>0}$, if and only if there exsits $H\leq G$ with index $m$.

What is this space homeomorphic to?

Prove that ${\rm Ker}f=\bigcap_{x\in G} xHx^{-1}$, where $H$ is a subgroup of the group $G$, and $f:G\to \text{Sym}(G/H)$ is the left-coset action.

Free action of a finite group gives a covering space

Why is $(12)(34).3 = 4?$

Name for subgroup of elements commuting with another group action

Division structure of a torsor

Reference Request: Groups acting on a topos

Problem $3E.1$ from Isaacs's "Finite group theory".

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