Order statistics-unique finite 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 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 |