The conjugacy problem and virtually cyclic subgroups in the Artin braid group quotient $B_n/[P_n,P_n]$

Abstract

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

16 pages. Comments are welcome

References in corpus (1)

• A fast solution to the conjugacy problem in the 4-strand braid group