# Finite group that is order statistics-equivalent to an abelian group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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## Definition

A finite group is termed a finite group that is order statistics-equivalent to an abelian group is a finite group that is order statistics-equivalent (i.e., has the same order statistics) to an abelian group (in particular, a finite abelian group.

Equivalently, it is a finite nilpotent group each of whose Sylow subgroups is a group of prime power order order statistics-equivalent to an abelian group.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions