# Group that is 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

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A **group that is 1-isomorphic to an abelian group** is a group that is 1-isomorphic to an abelian group.

See also finite group that is 1-isomorphic to an abelian group and group of prime power order 1-isomorphic to an abelian group.

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

abelian group | ||||

Baer Lie group | ||||

LCS-Baer Lie group | ||||

Lazard Lie group | ||||

LCS-Lazard Lie group | ||||

group of prime exponent | ||||

group of nilpotency class two whose commutator map is the double of an alternating bihomomorphism giving class two | ||||

group of nilpotency class two whose commutator map is the double of a skew-symmetric cyclicity-preserving 2-cocycle | ||||

group of nilpotency class two whose commutator map is the skew of a cyclicity-preserving 2-cocycle |