Coxeter-type quotients of surface braid groups

Let M be a closed surface, q ≥ 2 and n ≥ 2 . In this paper, we analyze the Coxeter-type quotient group B n ( M ) ( q ) of the surface braid group B n ( M ) by the normal closure of the element σ 1 q , where σ 1 is the standard Artin generator of the braid group B n . Also, we study the Coxeter-type quotient groups obtained by taking the quotient of B n ( M ) by the commutator subgroup of the respective pure braid group P n ( M ) , P n ( M ) and adding the relation σ 1 q = 1 , when M is a closed orientable surface or the disk.