List questions from group-actions

Published on 08 Dec 2018 - 14:25

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$\text{SL}_2(\mathbb Z)$ acts on upper plane $\mathbb H$. What kind of points have non-trivial stabilizer? And how many orbits are there?

Published on 25 Mar 2026 - 6:07

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Alternate definition of symmetric group action

Published on 25 Mar 2026 - 9:32

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$H$ is a subgroup of a finite group $G$ such that $|H|$ and $\big([G:H]-1\big)!$ are relatively prime. Prove that $H$ is normal in $G$.

Published on 25 Mar 2026 - 14:35

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Prove that an integration is left invariant.

Published on 25 Mar 2026 - 11:10

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Existence nontrivial Killing vector field $\iff$ existence nontrivial $\Bbb S^1$-action

Published on 14 Dec 2018 - 7:56

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Gromov norm and free $Z_2$-space

Published on 15 Dec 2018 - 9:40

397

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Coset space and orbit space of group action

Published on 16 Dec 2018 - 6:32

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Is every quotient by a finite group an orbifold?

Published on 19 Mar 2026 - 16:15

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Fundamental group action on universal cover chain complex

Published on 25 Mar 2026 - 20:34

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The action of $SO(n + 1)$ on $S^n$ is ergodic

Published on 26 Mar 2026 - 4:34

24

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Let $(a,z) \mapsto a*z=e^{ia}z$ be a application such that $a \in \mathbb{R}$ and $z \in S=\{ z \in \mathbb{C} : |z|=1\}$. Is this a faithful action?

Published on 19 Dec 2018 - 2:54

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Group action inverse?

Published on 20 Dec 2018 - 2:27

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Are the fixed point sets homeomorphic?

Published on 25 Mar 2026 - 13:32

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Proving group action on $GL_{n}(\mathbb{F})$

Published on 22 Dec 2018 - 15:20

List Question

Order of $C_{S_n}((12)(34)) \; \forall n\geq 4$ and its elements?

$\text{SL}_2(\mathbb Z)$ acts on upper plane $\mathbb H$. What kind of points have non-trivial stabilizer? And how many orbits are there?

Alternate definition of symmetric group action

$H$ is a subgroup of a finite group $G$ such that $|H|$ and $\big([G:H]-1\big)!$ are relatively prime. Prove that $H$ is normal in $G$.

Prove that an integration is left invariant.

Existence nontrivial Killing vector field $\iff$ existence nontrivial $\Bbb S^1$-action

Gromov norm and free $Z_2$-space

Coset space and orbit space of group action

Is every quotient by a finite group an orbifold?

Fundamental group action on universal cover chain complex

The action of $SO(n + 1)$ on $S^n$ is ergodic

Let $(a,z) \mapsto a*z=e^{ia}z$ be a application such that $a \in \mathbb{R}$ and $z \in S=\{ z \in \mathbb{C} : |z|=1\}$. Is this a faithful action?

Group action inverse?

Are the fixed point sets homeomorphic?

Proving group action on $GL_{n}(\mathbb{F})$

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