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?

  • $\begingroup$ 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". $\endgroup$ – Derek Holt Jul 18 at 10:04
  • $\begingroup$ This also means that all points have the same stabilizer. $\endgroup$ – YCor Jul 18 at 14:07

Yes, it's called effectively free (see for instance here, page 3, Fels/Olver, On relative invariants).

  • $\begingroup$ Yves, many thanks! $\endgroup$ – R W Jul 18 at 10:29

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