Permutation group

A permutation group is a concept with an attitude essentially corresponding to a faithful group action. Specifically, a permutation group $𝐺$ is a subgroup of the symmetric group $Ω!$ for some ground set $Ω$ . group Since by Cayley’s theorem every group can be made into a permutation group, the point is that $𝐺$ is equipped with a canonical action on $Ω$ .