# Order statistics-equivalence is finite-direct product-closed

From Groupprops

## Contents

## Statement

### Statement for direct product of two groups

Suppose are finite groups such that is order statistics-equivalent to and is order statistics-equivalent to . Then, the External direct product (?) is order statistics-equivalent to the external direct product .

Here, two finite groups are termed order statistics-equivalent finite groups if they have the same order statistics, i.e., the same number of elements of each order.

### Statement for direct product of finitely many groups

Suppose and are groups such that, for each satisfying , is order statistics-equivalent to . Then, the External direct product (?) is order statistics-equivalent to .