## Lie group action with no slice

Let $x\in M$, $M$ - finite dimensional smooth manifold. Is there an example of a finite dimensional Lie group action on $M$ with no slice at $x$?

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Please read mathoverflow.net/howtoask and revise this question. – Theo Johnson-Freyd Jan 13 at 5:08

The action of $\mathbb{R}$ on $\mathbb{R}^2$ by $(x,y)\mapsto (x,y+ax)$ is also a classic. The y-axis is fixed, but has no slice. – Ben Webster Jan 13 at 17:03