Some subgroups of Artinʹs braid group

Let Bn be the braid group on n strings and let Φn : Bn → Sn be the standard homomorphism of Bn 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 Bn,P of Bn whose image Φn(Bn,P) in Sn preserves a partition P of the set }1,…,n}.