A group is termed parafree if it is residually nilpotent and has the same nilpotent quotients as a given free group. The object
of this paper is, in the main, to survey some of the known results about parafree groups, to record several new ones and to
discuss some old and new open problems.
Keywords Parafree group - free (non-abelian) group - residually nilpotent group - lower central series - lower central sequence - one-relator group - HNN extension