List questions from group-actions

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How to prove or disprove the expression of the index of a subgroup?

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A fundamental domain for any reductive group from that of $\operatorname{GL}_n(\mathbb R)$

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In a group $G$ acting on a set $X$, can $X$ have indistinguishable elements?

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What group action underpins the quotient by a group action in this answer?

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Problem 4.3.1 from Dummit and Foote.

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Group of isometries acting on a metric space is already discrete if a stabilizer is finite and an orbit is discrete

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$[G:H]=\sum[K:(K\cap gHg^{-1})]$

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Action on identity in crossed modules

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$G$, $H$ groups. Why not caring about $G$-actions on $H$ s.t. $\phi_g\in{\rm{Sym}}(H)\setminus{\rm{Aut}}(H)$ for some $g\in G\setminus\{e\}$?

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How to determine regular subgroup

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A variation of Sylow's counting theorem

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Notation explanation: $\Omega(G)$

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Question regarding order of evaluation of elements in Group Action example

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Topological groups acting on sets

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List Question

Induced group action on cohomology of vector bundle

How to prove or disprove the expression of the index of a subgroup?

A fundamental domain for any reductive group from that of $\operatorname{GL}_n(\mathbb R)$

In a group $G$ acting on a set $X$, can $X$ have indistinguishable elements?

What group action underpins the quotient by a group action in this answer?

Problem 4.3.1 from Dummit and Foote.

Group of isometries acting on a metric space is already discrete if a stabilizer is finite and an orbit is discrete

$[G:H]=\sum[K:(K\cap gHg^{-1})]$

Action on identity in crossed modules

$G$, $H$ groups. Why not caring about $G$-actions on $H$ s.t. $\phi_g\in{\rm{Sym}}(H)\setminus{\rm{Aut}}(H)$ for some $g\in G\setminus\{e\}$?

How to determine regular subgroup

A variation of Sylow's counting theorem

Notation explanation: $\Omega(G)$

Question regarding order of evaluation of elements in Group Action example

Topological groups acting on sets

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