The Chen Groups of the Pure Braid Group

作者: Alexander I. Suciu , Daniel C. Cohen

DOI:

关键词:

摘要: Ab stract. The Chen groups of a group are the lower central series quotients its maximal metabelian quotient. We show that pure braid Pn free abelian, and we compute their ranks. computation these reduces to Hilbert certain graded module over polynomial ring, latter is carried out by means Groebner basis algorithm. This result shows that, for n‚ 4, not direct product groups.

参考文章(20)
Toshitake Kohno, Takayuki Oda, The Lower Central Series of the Pure Braid Group of an Algebraic Curve Galois Representations and Arithmetic Algebraic Geometry. pp. 201- 219 ,(1987) , 10.2969/ASPM/01210201
Fred Cohen, The homology of Cn+1-Spaces, n≥0 Springer Berlin Heidelberg. pp. 207- 351 ,(1976) , 10.1007/BFB0080467
Hiroaki Terao, Peter Orlik, Arrangements of hyperplanes ,(1992)
Jonathan A. Hillman, Alexander Ideals of Links ,(1981)
Paul E. Schupp, Roger C. Lyndon, Combinatorial Group Theory ,(1977)
Ferdinando Mora, An Algorithm to Compute the Equations of Tangent Cones EUROCAM '82 Proceedings of the European Computer Algebra Conference on Computer Algebra. pp. 158- 165 ,(1982) , 10.1007/3-540-11607-9_18
Egbert Brieskorn, Sur les groupes de tresses Séminaire Bourbaki. ,vol. 14, pp. 21- 44 ,(1972)
Michael Falk, Richard Randell, The lower central series of a fiber-type arrangement. Inventiones Mathematicae. ,vol. 82, pp. 77- 88 ,(1985) , 10.1007/BF01394780
A. Libgober, On the homology of finite Abelian coverings Topology and its Applications. ,vol. 43, pp. 157- 166 ,(1992) , 10.1016/0166-8641(92)90137-O