- Thread starter
- #1

**Problem statement:** Let $G$ act on $X$, and suppose $x,y\in X$ are in the same orbit for this action. How are the stabilizer subgroups $G_x$ and $G_y$ related?

**My attempt:** $G_x = G_y = \{g \in G: gx=x\} = \{g \in G: gy=y\} \forall x,y \in X, \forall g \in G$.

Thanks.