Editing Cayley's theorem (section)

==Remarks on the regular group representation==
The identity element of the group corresponds to the identity permutation. All other group elements correspond to [[derangements]]: permutations that do not leave any element unchanged. Since this also applies for powers of a group element, lower than the order of that element, each element corresponds to a permutation that consists of cycles all of the same length: this length is the order of that element. The elements in each cycle form a right [[coset]] of the subgroup generated by the element.