New posts in Group Actions

Intuition behind picking group actions and Sylow

Why is left multiplication on a group bijective?

Are there non-homogeneous topological spaces which are "almost homogeneous" in Rudin's sense?

Extending the action $S_5$ on $2$-subsets of $\{1,\cdots,5\}$ to an action of $S_6$.

Sharply $k$-transitive actions on spheres

Invariant subspaces to the permuting action of the alternating group.

How to convince myself (imagine) that $\Bbb S^1$-action on $\Bbb S^3$ fixes a circle of sphere?

Let $G$ be a group with $33$ elements acting on a set with $38$ elements. Prove that the stabilizer of some element $x$ in $X$ is all of $G$.

(Proof verification) For each $s \in S$, show that $\sum_{t \in Gs} \frac{1}{|Gt|}=1$

Let $H$ be a subgroup of $G$, and suppose that $G$ acts by multiplication over the set $X:=G/H$ of the left-hand side classes of $H$ over $G$.