Tree groups and the 4-string pure braid group

The Chen Groups of the Pure Braid Group

A b st r ac t . 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 Pn 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 o...

The Chen Groups of the Pure Braid Group DANIEL

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 Pn 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 bas...

Derivative Varieties and the Pure Braid Group

The Chen Groups of the Pure Braid

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 Pn 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 bas...

Efficient Group Key Agreement on Tree-based Braid Groups

The security issues in ad hoc network are increasingly important. In this paper, we propose a distributed key management what approach by using braid groups and key tree. Without any assumption of prefixed trust relationship between nodes, the proposed method works in a self-organizing way to provide the key management services. The using of the proposed tree-based braid groups has following ad...