# Order statistics-unique finite group

From Groupprops

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

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A finite group is termed **order statistics-unique** if there is no other finite group that is order statistics-equivalent to it, i.e., there is no other finite group having the same order statistics.

## Relation with other properties

### Stronger properties

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

Finite cyclic group | finite group having the same order statistics as a cyclic group is cyclic | |FULL LIST, MORE INFO | ||

Finite elementary abelian 2-group | exponent two implies abelian |