Free Differential Calculus, IV. The Quotient Groups of the Lower Central Series

  title={Free Differential Calculus, IV. The Quotient Groups of the Lower Central Series},
  author={K. T. Chen and Ralph Hartzler Fox and Roger Lyndon},
  journal={Annals of Mathematics},
The quotient groups Qn(G) =GnGn+i of the lower central series G = G1 D G, D G, D * * of a finitely generated group G are finitely generated abelian groups. Our object is to develop an algorithm for the calculation of Qn from any given finite presentation of G. As a preliminary step, the special case of a free group X is considered. It is known [2], [7] that, for a free group X of rank q, the group Qn(X) is a free abelian group whose rank is the Witt number 0b,(q), and a basis for QJ(X) has been… Expand
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