Group of prime power order 1-isomorphic to an abelian 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 group of prime power order 1-isomorphic to an abelian group is a group of prime power order that is 1-isomorphic to an abelian group (in particular, to an abelian group of prime power order).

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Abelian group of prime power order
Finite p-group of nilpotency class less than p