We have seen in class that if we fix a group $G$ and a set $X$, to give an action of $G$ on $X$ is equivalent to give a morphism of groups from $G$ to the group $\text{Bij}(X,X)$ of all bijections from $X$ to itself.
I mean that this is nice in some way, but I don't see where this can be useful, so I know how to go from one side to the other but could someone maybe give me an example where this can be used? Maybe it would be helpful to start with an "easy" one since it will be the first example I have seen about this statement.
Thanks for your help.