# Order-cum-power statistics of a finite group

From Groupprops

## Contents

## Definition

Let be a finite group. The **order-cum-power statistics** of give information about the number of elements of any given order that are powers of a certain kind. More precise formulations are given below.

In all the versions below, we let be the order of and be the set of natural numbers dividing .

### Doubly cumulative version

In this version, the statistics are given by the following function : is the number of elements such that is the identity element and there exists such that .

## Related notions

If two finite groups have the same order-cum-power statistics, we say that they are order-cum-power statistics-equivalent finite groups.