# Finite group in which all cumulative order statistics values divide the order of the 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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A finite group in which all cumulative order statistics values divide the order of the group is a finite group $G$with the following property: for every natural number $d$, the number of elements $g$ such that $g^d$ is the identity element is a divisor of the order of $G$.

In other words, a finite group in which all the values in the cumulative version of the order statistics divide the order of the group. Thus, to evaluate whether this property holds for a group, we simply need to know the order statistics of the group.

## Relation with other properties

### Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
finite abelian group
finite group that is 1-isomorphic to an abelian group
finite group that is order statistics-equivalent to an abelian group
finite p-group in which the number of nth roots is a power of p for all n