In mathematics, an action of a group G {\displaystyle G} on a set S {\displaystyle S} is, loosely speaking, an operation that takes an element of G {\displaystyle G} and an element of S {\displaystyle S} and produces another element of S . {\displaystyle S.} More formally, it is a group homomorphism from G {\displaystyle G} to the automorphism group of S {\displaystyle S} (the set of all bijections on S {\displaystyle S} along with group operation being function composition).
In mathematics, an action of a group G {\displaystyle G} on a set S {\displaystyle S} is, loosely speaking, an operation that takes an element of G {\displaystyle G} and an element of S {\displaystyle S} and produces another element of S . {\displaystyle S.} More formally, it is a group homomorphism from G {\displaystyle G} to the automorphism group of S {\displaystyle S} (the set of all bijections on S {\displaystyle S} along with group operation being function composition).
Source: Wikipedia "Group action" · CC BY-SA 4.0
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