Some Subgroups of Artin's Braid Group

Let B_n be the braid group on n strings and let Phi(n):B_n --> S_n be the standard homomorphism of B_n onto the group of permutations of the set {1,...,n}. In this paper the author calculates, using the Reidemeister-Schreier method, a presentation for the subgroups B_n,B_P of B_n whose image Phi(n)(B_n,B_P) in S_n preserves a partition P of the set {1,...,n}