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

Oscar Ocampo; Paulo Cesar Cerqueira dos Santos J\'unior

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

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arxiv 2109.00390 v1 pith:HMGN3N3N submitted 2021-09-01 math.GR math.GT

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

Oscar Ocampo , Paulo Cesar Cerqueira dos Santos J\'unior This is my paper

classification math.GR math.GT

keywords artinbraidgroupconjugacycyclicproblemquotientsubgroups

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Let $n\geq 3$. 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 $B_n/[P_n,P_n]$.

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

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