# Actions that become free after quotienting out their kernel

Let $$H$$ be the kernel of an action of a group $$G$$ on a space $$X$$. Is there a term for the actions with the property that the action of the quotient group $$G/H$$ on $$X$$ is free?

• The induced action of $G/H$ on $X$ is the image of the action of $G$ on $X$ under the homomorphism that defines the action, so you could say "actions with free image". – Derek Holt Jul 18 at 10:04
• This also means that all points have the same stabilizer. – YCor Jul 18 at 14:07