Examples

• In S₃ all elements are cycles. The identity element e is a 0- or 1-cycle, the other elements are 2- or 3-cycles: (1,2), (1,3), (2,3), (1,2,3) and (1,3,2). No two of these 5 cycles are disjoint.
• In S₄, the element (in list notation) [2, 1, 4, 3] is not a cycle, but it is the product (1,2)(3,4) of the transpositions (1,2) and (3,4).