List questions from group-actions

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Group actions and invariant subspaces

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List Question

Cohomology of $G$-invariant differential forms

Some actions on simple space may be non-trivial.

Intuitive idea behind orbit stabilizer theorem.

Dimension of orbit of a one-dimensional vector under action of $SO(n)$

Group action such that $H^1(G, L^{\times}) \neq \{1\}$.

If $A^\Gamma$ is finite why is $A/(\gamma-1)A$ trivial?

Showing group action consists of homomorphisms

On proving that a finitely generated group has a finite number of subgroups with index $n$.

Exercises with homeomorphism group action on $\mathbb R^2$

Module endomorphisms

Centralizer of a Sylow group in the simple group of order 360

Image of an involution under Cayley action in $A_n$

Action of the dihedral group $D_{2n}$ on vertex set of regular $n$-gon is primitive $\iff\,n$ is prime?

Show a $G$-set $(X,\mu: X\times G\to X)$ has continuous $\mu$ iff for each $x\in X$ its isotropy group is open.

Group actions and invariant subspaces

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