I'm interested in when (and how) the modern idea of a group action developed and how group actions became their own algebraic structures.
As far as I can tell in the 19th century group actions were much more implicit than they are today and were strongly tied to the group itself, as a subgroup of a permutation group. But the way group actions are presented today (at the very least as they were presented to me) is much more axiomatic and considers group actions and groups as separate algebraic structures.
When and how did this change (if it changed at all) and how did group actions become so important?
I'm also looking for books or articles on this topic, so it would be very much appreciated if anyone has a recommendation, as the books on the history of group theory I have skimmed don't mention the development of group actions.