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TitleThe Chen groups of the pure braid group
Author(s) Daniel C. Cohen, Alexander I. Suciu
TextD. 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. 45--64.
TypeBook, Chapter in Book, Conference Proceeding
AbstractThe 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.
Keywordslower central series; Chen groups; pure braid groups; Hilbert series; graded modules; Gröbner bases
URL http://www.math.neu.edu/~suciu/papers/chenpn.pdf
SeriesContemporary Mathematics
PublisherAmerican Mathematical Society
AddressProvidence, RI
EditorMila Cenkl and Haynes Miller
Translation No
Refereed Yes
ConferencenameThe \v Cech centennial, a Conference on Homotopy Theory held at Northeastern University, Boston, Massachusetts, June 22--26, 1993