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
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
A finite group in which all cumulative order statistics values divide the order of the group is a finite group with the following property: for every natural number , the number of elements such that is the identity element is a divisor of the order of .
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
|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|