A group action is free if for every $x\in X$ the stabilizer group $G_x=Stab_G(x)=\{g \in G: x \cdot g=x\}$ 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.
$\blacksquare$
(see @sharpe2000differential Proposition 2.2 page 145).
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Author of the notes: Antonio J. Pan-Collantes
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