Parafree group

Definition
A group $$G$$ 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:


 * 1) It is a defining ingredient::residually nilpotent group.
 * 2) There exists a defining ingredient::free group $$F$$ 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 $$i$$, $$\varphi$$ induces an isomorphism $$\gamma_i(F)/\gamma_{i+1}(F) \cong \gamma_i(G)/\gamma_{i+1}(G)$$.