The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient Bn/[Pn,Pn

Abstract

Let n≥3. In this paper we deal with the conjugacy problem in the Artin braid group quotient Bn/[Pn,Pn]. To solve it we use systems of equations over the integers arising from the action of Bn/[Pn,Pn] over the abelianization of the pure Artin braid group Pn/[Pn,Pn]. Using this technique we also realize explicitly infinite virtually cyclic subgroups in Bn/[Pn,Pn].