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If I am given a vector space (e.g. [itex]\mathbb{R}^n[/itex]), and a group [itex]G[/itex] that acts on [itex]\mathbb{R}^n[/itex], what are the conditions that [itex]G[/itex] must satisfy so that for any given [itex]x\in\mathbb{R}^n[/itex] its orbit [itex]Gx[/itex] is amanifold?

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# Question on group actions on vector spaces

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