Finite group that is order statistics-equivalent to an abelian group

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Definition

A finite group is termed a finite group that is order statistics-equivalent to an abelian group is a finite group that is order statistics-equivalent (i.e., has the same order statistics) to an abelian group (in particular, a finite abelian group.

Equivalently, it is a finite nilpotent group each of whose Sylow subgroups is a group of prime power order order statistics-equivalent to an abelian 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 admitting a bijective quasihomomorphism to an abelian group|FULL LIST, MORE INFO
Finite group that is 1-isomorphic to an abelian group |FULL LIST, MORE INFO
Group of prime power order order statistics-equivalent to an abelian group

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Finite group in which all cumulative order statistics values divide the order of the group
Finite nilpotent group