List questions from group-actions

Published on 04 Apr 2026 - 7:56

39

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Stabilizer of action $PGL_n(\mathbb{R})$ on $\mathbb{PR}^{n-1}$

Published on 27 Sep 2021 - 15:02

541

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Prove that $\pi(x)$ is a product of $m$ $n$-cycles.

Published on 27 Sep 2021 - 15:52

360

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Let $G$ act transitively on a set $A$. Show that if there is some $\alpha\in A$ such that $G_\alpha=\{1\}$, then $G_\beta=\{1\}$ for all $\beta\in A$

Published on 27 Sep 2021 - 21:49

139

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Subobject classifier in $BG$

Published on 01 Apr 2026 - 19:16

230

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$GL_n$($ℂ$) acts on the set $Mat_n$(ℂ) by conjugation

Published on 30 Sep 2021 - 16:05

49

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An injection of double cosets

Published on 30 Sep 2021 - 19:28

218

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Double connectedness of SO3 via action on S2

Published on 31 Mar 2026 - 6:06

116

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If $(g,a) \mapsto g \cdot a$ is an action of $G$ on $A$ and $H \vartriangleleft G$, is $(\overline{g},a) \mapsto g \cdot a$ an action of $G/H$ on $A$?

Published on 29 Mar 2026 - 5:12

163

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Consider the action of $S_3$ on itself by conjugation. Describe the orbits of (1, 2) and (1, 2, 3) under this action.

Published on 07 Apr 2026 - 21:39

96

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Group action on one-dimensional subspaces

Published on 27 Mar 2026 - 1:13

135

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transitive subgroup of an action

Published on 04 Oct 2021 - 11:35

90

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A regular subset of a transitive group

Published on 04 Oct 2021 - 17:06

61

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Is there a smooth non-trivial action of $\mathrm{SU}(2)$ on a torus $\mathbb{T}^k$ for $k> 2$?

Published on 05 Oct 2021 - 10:55

90

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A generalisation of the Artin-Tate Lemma

Published on 05 Oct 2021 - 22:43

List Question

Number of the group homomorphisms $G\to S_3$, where $|G|=8$

Stabilizer of action $PGL_n(\mathbb{R})$ on $\mathbb{PR}^{n-1}$

Prove that $\pi(x)$ is a product of $m$ $n$-cycles.

Let $G$ act transitively on a set $A$. Show that if there is some $\alpha\in A$ such that $G_\alpha=\{1\}$, then $G_\beta=\{1\}$ for all $\beta\in A$

Subobject classifier in $BG$

$GL_n$($ℂ$) acts on the set $Mat_n$(ℂ) by conjugation

An injection of double cosets

Double connectedness of SO3 via action on S2

If $(g,a) \mapsto g \cdot a$ is an action of $G$ on $A$ and $H \vartriangleleft G$, is $(\overline{g},a) \mapsto g \cdot a$ an action of $G/H$ on $A$?

Consider the action of $S_3$ on itself by conjugation. Describe the orbits of (1, 2) and (1, 2, 3) under this action.

Group action on one-dimensional subspaces

transitive subgroup of an action

A regular subset of a transitive group

Is there a smooth non-trivial action of $\mathrm{SU}(2)$ on a torus $\mathbb{T}^k$ for $k> 2$?

A generalisation of the Artin-Tate Lemma

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