List questions from group-actions

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The group G acts faithfully on X

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Characterisation of proper group actions

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Finding explicit elements in $\text{SL}(3,\mathbb{R})/\text{SO}(3)$ whose simultaneous stabilizer in $\text{SL}(3,\mathbb{R})$ is the identity

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understanding the homogeneous space $SL(2,\mathbb C)\times \mathbb C\cong SU(2)\times S^1$?

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Orbits and alternating groups

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Suppose $g,h,a∈G$ such that $h=aga^{−1}$. Prove that the formula $x↦ax$ defines a bijection of sets $Fix_X(g)→Fix_X(h)$

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Complete length space with discrete action

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Show that the real axis and the upper half plane are mapped to themselves under $SL(2, \Bbb R)$

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Orbit maps are proper if and only if action is proper?

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Well-definedness of induced representation

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List Question

If two group actions on a set are both transitive, must they be the same?

Correspondence of grading and group actions

The group G acts faithfully on X

Characterisation of proper group actions

Finding explicit elements in $\text{SL}(3,\mathbb{R})/\text{SO}(3)$ whose simultaneous stabilizer in $\text{SL}(3,\mathbb{R})$ is the identity

understanding the homogeneous space $SL(2,\mathbb C)\times \mathbb C\cong SU(2)\times S^1$?

Orbits and alternating groups

Functions between G-set and H-set

Switching the components of $G\times G$

Group Orbits of this space under O(3)

Suppose $g,h,a∈G$ such that $h=aga^{−1}$. Prove that the formula $x↦ax$ defines a bijection of sets $Fix_X(g)→Fix_X(h)$

Complete length space with discrete action

Show that the real axis and the upper half plane are mapped to themselves under $SL(2, \Bbb R)$

Orbit maps are proper if and only if action is proper?

Well-definedness of induced representation

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