the wider definition of a cyclic permutation, allowing fixed points, these fixed points each constitute trivial orbits of the permutation, and there is a single non-trivial orbit containing all the remaining points. This can be used as a definition: a cyclic permutation (allowing fixed points) is a permutation that has a single non-trivial orbit. Every permutation on finitely many elements can be decomposed into cyclic permutations whose non-trivial orbits are disjoint.

The individual