Order statistics-unique finite group

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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 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