Free group action

A group action is free if for every $x\in X$ the stabilizer group $G_x=Sta{b}_G(x)=\{g\in G:x\cdot g=x\}$ is the trivial subgroup $\{1\}$.

Proposition
Given a Lie group $G$ and a closed subgroup $H$ then the right action of $H$ on $G$ is free.
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(see @sharpe2000differential Proposition 2.2 page 145).