Answer by Someone for Action of a Lie group on a smooth manifold
So I am going to do this step by step. So I belive it's clear that $G_p$ is a closed subgroup of $G$, and we can consider the proper free action $G\times G_p\rightarrow G_p$ by left translation , and...
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Suppose a Lie group acts smoothly (but not necessarily properly or freely)on a smooth manifold $M$. Show that each orbit is an immersed submanifoldof $M$; which is embedded if the action is proper.This...
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