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
A group is termed parafree (sometimes also absolutely parafree to distinguish from the relative notion thati s useful when dealing with subvarieties of the variety of groups) if it satisfies both these conditions:
- It is a residually nilpotent group.
- There exists a free group and a homomorphism of groups that induces identity maps on each quotient group between successive members of the lower central seriesExplicitly, for every positive integer , induces an isomorphism .
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|