Remark

The order of a permutation is related to periodic phenomena, in the sense of repeated patterns. For instance, if g is a permutation of order 5 in S_n, then for every permutation h in S_n, the sequence of permutations

h, gh, g²h, g³h, g⁴h, g⁵h, g⁶h, ...

is periodic, since g⁵ = e, g⁶ = g, etc.