List questions from group-actions

Published on 10 Apr 2026 - 14:48

568

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Proving the stabilizer of an element in a group is a subgroup

Published on 10 Jul 2022 - 19:25

220

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Proving the kernel of a group action is the intersection of all the stabilizers

Published on 10 Jul 2022 - 19:34

205

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Proving the set of orbits of the action of a group on a set form a partition of that set

Published on 10 Jul 2022 - 20:27

330

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Proving the action of a group on a set is transitive if and only if $G \cdot x = X$

Published on 10 Jul 2022 - 21:09

201

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Action of finite group on a set of subgroups is transitive

Published on 11 Jul 2022 - 10:41

69

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Show the following action preserves the set $X = \{(g_1,...,g_p) \in G^p \mid g_1g_2 \cdots g_p = e \}$

Published on 11 Jul 2022 - 21:09

137

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Prove that $G_3$ acts on the set of opposite edges of a tetrahedron

Published on 12 Jul 2022 - 0:14

26

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For which $G$ can $d_{\mathbb{R}^N/G}(x,y)$ be computed quickly?

Published on 13 Jul 2022 - 1:26

239

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For the set $X=\{g\in G:g^p=1\}$, show that $p$ divides $|X|$.

Published on 13 Jul 2022 - 23:06

282

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Left action and group automorphism

Published on 09 Apr 2026 - 7:50

243

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Left Translation Action is Ergodic with respect to Haar

Published on 24 Feb 2026 - 13:10

96

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Is there a group action which is not free but induces covering map?

Published on 08 Apr 2026 - 18:43

28

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Does every effective $T^4$-action on a simply connected 6-manifold admit a free subtorus action?

Published on 25 Mar 2026 - 23:37

53

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Notion of $G$-stable subsets in Moerdijk and Mrčun's Introduction to foliations and Lie groupoids

Published on 09 Apr 2026 - 15:45

List Question

Can we think of rotations in $\mathbb R^3$ as translations in some sense?

Proving the stabilizer of an element in a group is a subgroup

Proving the kernel of a group action is the intersection of all the stabilizers

Proving the set of orbits of the action of a group on a set form a partition of that set

Proving the action of a group on a set is transitive if and only if $G \cdot x = X$

Action of finite group on a set of subgroups is transitive

Show the following action preserves the set $X = \{(g_1,...,g_p) \in G^p \mid g_1g_2 \cdots g_p = e \}$

Prove that $G_3$ acts on the set of opposite edges of a tetrahedron

For which $G$ can $d_{\mathbb{R}^N/G}(x,y)$ be computed quickly?

For the set $X=\{g\in G:g^p=1\}$, show that $p$ divides $|X|$.

Left action and group automorphism

Left Translation Action is Ergodic with respect to Haar

Is there a group action which is not free but induces covering map?

Does every effective $T^4$-action on a simply connected 6-manifold admit a free subtorus action?

Notion of $G$-stable subsets in Moerdijk and Mrčun's Introduction to foliations and Lie groupoids

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