The order of an element a in a group G is the least positive integer n such that ⁠ a n = e ⁠, where a n represents a ⋯ ⋯ a ⏟ ⏟ n factors , that is, application of the operation " ⁠ ⋅ ⋅ ⁠ " to n copies of ⁠ a ⁠. (If " ⁠ ⋅ ⋅ ⁠ " represents multiplication, then a n corresponds to the ⁠ n ⁠ th power of ⁠ a ⁠.) In infinite groups, such an n may not exist, in which case the order of a is said to be infinity. The order of an element equals the order of the cyclic subgroup generated by this element.