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Recall that a compact manifold $M$ with a $G$-action, where $G$ is a compact Lie group, is such that $M$ contains an open, dense and convex subset where the points have the smaller possible isotropy group.

Assuming the action is effective, does $M$ has a point with trivial isotropy?

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This is false.

Consider the $SO(3)$ action on $S^2$. It is effective but every point has isotropy.

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