Details:
Title  The Chen groups of the pure braid group  Author(s)  Daniel C. Cohen, Alexander I. Suciu  Text  D. Cohen, A. Suciu, The Chen groups of the pure braid group, In: The Cech
Centennial: A Conference on Homotopy Theory (M. Cenkl, H. Miller, eds.),
Contemp. Math., vol. 181, Amer. Math. Soc., Providence, RI, 1995, pp. 4564.  Type  Book, Chapter in Book, Conference Proceeding  Abstract  The Chen groups of a group are the lower central series quotients of its maximal metabelian quotient. We show that the Chen groups of the pure braid group P_n are free abelian, and we compute their ranks. The computation of these Chen groups reduces to the computation of the Hilbert series of a certain graded module over a polynomial ring, and the latter is carried out by means of a Gröbner basis algorithm. This result shows that, for n>=4, the group P_n is not a direct product of free groups.
 Keywords  lower central series; Chen groups; pure braid groups; Hilbert series; graded modules; Gröbner bases  Length  20  ISBN  0821802968 
URL 
http://www.math.neu.edu/~suciu/papers/chenpn.pdf 
Language  English  Series  Contemporary Mathematics  Volume  181  Pages  4564  Publisher  American Mathematical Society  Address  Providence, RI  Year  1995  Editor  Mila Cenkl and Haynes Miller  Translation 
No  Refereed 
Yes  Conferencename  The \v Cech centennial, a Conference on Homotopy Theory held at Northeastern University, Boston, Massachusetts, June 2226, 1993 
