# Power statistics of a finite group

From Groupprops

## Definition

The **power statistics** of a finite group of order can be viewed in the following ways:

- The
*non-cumulative*power statistics is a function from the set of divisors of to the nonnegative integers, which sends to the number of elements for which there exists satisfying but such that there is no*larger*divisor of for which there exists with . - The
*cumulative*power statistics is a function from the set of divisors of to the nonnegative integers, which sends to the number of elements for which there exists satisfying .

## Related notions

### Similar statistics

- Order statistics of a finite group: This gives information on the number of elements of each order.
- Order-cum-power statistics of a finite group: This gives information on the number of elements of a given order that arise as given powers.