Group that is 1-isomorphic to an abelian group
From Groupprops
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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 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.
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 |
