# Set of orders of a finite group

From Groupprops

*This article talks about a statistics, which could be a function or a set of numbers, associated with any finite group*

## Definition

Let be a finite group. Then, the *set of orders* of is the subset of comprising those elements for which there is at least one element in of order .

The set of orders of a finite group is closely related to its order statistics. More precisely the set of orders is that subset of the nonnegative integers for which the order statistics function takes positive values.