List questions from group-actions

Published on 03 Apr 2026 - 5:23

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Let $G$ a group and $A=G$, prove that the maps defined by $g\cdot a =ag^{-1}$ for all $g, a\in G$ satisfy the axioms of a left group action.

Published on 12 Oct 2017 - 9:49

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How many orbits does there exist if $\forall g \in GL(E), \forall v \in E, g \cdot v = g(v) $?

Published on 13 Oct 2017 - 13:30

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Prove the size of the conjugacy class of $x$ is equal to the index of $C(x)$ in $G$.

Published on 14 Oct 2017 - 8:18

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Invariants of an action of $\mathsf{SL}_2$ on a space of homogeneous polynomials related to cross-ratio

Published on 26 Mar 2026 - 14:34

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Are stabilizers of elements of the same orbit equal?

Published on 14 Oct 2017 - 19:51

280

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Point stabilizers and automorphisms

Published on 30 Mar 2026 - 16:58

96

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Discrete subgroup of homeomorphisms acts properly

Published on 02 Apr 2026 - 9:15

59

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group oaction of $GL(n,\mathbb{R})$ on $\mathbb{R}^n$

Published on 17 Oct 2017 - 17:35

518

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Closure of an orbit and quotient topology

Published on 01 Apr 2026 - 1:06

43

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How to find all the blocks containing any specific element?

Published on 20 Oct 2017 - 5:56

66

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Non-trivial blocks when $S_n$ acts naturally on $[n]$.

Published on 20 Oct 2017 - 7:52

233

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Regular primitive permutation groups

Published on 20 Oct 2017 - 14:03

114

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Let group $G$ acts on set $M$. Why are there always $\# G_m$ elements in $G$ map $m$ into any $n$ in the orbit $G\cdot m$?

Published on 20 Oct 2017 - 14:30

96

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Ergodicity of group action on a generating family

Published on 01 Apr 2026 - 1:06

List Question

Cohomology of an orbit space

Let $G$ a group and $A=G$, prove that the maps defined by $g\cdot a =ag^{-1}$ for all $g, a\in G$ satisfy the axioms of a left group action.

How many orbits does there exist if $\forall g \in GL(E), \forall v \in E, g \cdot v = g(v) $?

Prove the size of the conjugacy class of $x$ is equal to the index of $C(x)$ in $G$.

Invariants of an action of $\mathsf{SL}_2$ on a space of homogeneous polynomials related to cross-ratio

Are stabilizers of elements of the same orbit equal?

Point stabilizers and automorphisms

Discrete subgroup of homeomorphisms acts properly

group oaction of $GL(n,\mathbb{R})$ on $\mathbb{R}^n$

Closure of an orbit and quotient topology

How to find all the blocks containing any specific element?

Non-trivial blocks when $S_n$ acts naturally on $[n]$.

Regular primitive permutation groups

Let group $G$ acts on set $M$. Why are there always $\# G_m$ elements in $G$ map $m$ into any $n$ in the orbit $G\cdot m$?

Ergodicity of group action on a generating family

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