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Autori: D.C. Cohen, A.I. Suciu
Editorial: The Cech centennial (Boston, MA, 1993), M. Cenkl, H. Miller, American Mathematical Society, Contemporary Mathematics, 181, p.45-64, 1995.
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 Groebner basis algorithm. This result shows that, for n ge 4, the group P_n is not a direct product of free groups.
Cuvinte cheie: Lower central series, Chen groups, pure braid groups, Hilbert series, Groebner basis