Hey, We can define a group action in two ways:

1) A group G is said to act on a set X, if there exists agroup homomorphismψ : G --> S(X) [the symmetric group of X].

2)Equivalently, a group G acts on a set X, if there is a map from G x X --> X which assigns to each ordered pair <g,x>--->g.x, such that :

For all x Є X, e.x = x

(h.g).(x) = h.(g.x), where h, g Є G, and x Є X

How are these two definitions equivalent?