# Power statistics of a finite group

Jump to: navigation, search

## Definition

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

1. The non-cumulative power statistics is a function from the set of divisors of $n$ to the nonnegative integers, which sends $d$ to the number of elements $g \in G$ for which there exists $h \in G$ satisfying $h^d = g$ but such that there is no larger divisor $d'$ of $n$ for which there exists $k \in G$ with $k^{d'} = g$.
2. The cumulative power statistics is a function from the set of divisors of $n$ to the nonnegative integers, which sends $d$ to the number of elements $g \in G$ for which there exists $h \in G$ satisfying $h^d = g$.