# Group that is 1-isomorphic to an abelian group

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 properties
VIEW 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.

## 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