# Changes

The '''order statistics''' of a [[finite group]] is a function $\mathbb{N}_0 \to \mathbb{N}_0$ which takes $n$ and outputs the number of elements $x$ whose order is $n$.
If $f$ denotes the order statistics function, then the [[number:Dirichlet convolution|Dirichlet convolution ]] $F = f * U$ gives, for each $n$, the number of elements $x$ satisfying $x^n = e$. Two finite groups that have the same order statistics are termed [[order statistics-equivalent finite groups]].