Exponent

For a finite group, the exponent is the least common multiple of the orders of all elements; more generally it is the smallest positive integer n such that g^n = e for every element g when such an integer exists, otherwise the group is said to have infinite exponent.

The exponent of an algebraic structure (commonly a group) is the least common multiple of the orders of all its elements, equivalently the smallest positive integer m such that x^m equals the neutral element for every element x; if no such m exists the exponent is said to be infinite.