Parafree group

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 $G$ is termed parafree if it satisfies both these conditions:

1. It is a residually nilpotent group.
2. There exists a free group $F$ such that each quotient group between successive members of the lower central series of $F$ is isomorphic to the corresponding quotient for $G$. Explicitly, for every positive integer $i$, ${\gamma }_i(F)/{\gamma }_{i+1}(F)\cong {\gamma }_i(G)/{\gamma }_{i+1}(G)$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
free group