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.


Parafree group free (non-abelian) group residually nilpotent group lower central series lower central sequence one-relator group HNN extension 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Gilbert Baumslag
    • 1
  1. 1.Department of Mathematics, City College of New YorkCity University of New YorkNew YorkUSA

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