On p-almost direct products and residual properties of pure braid groups of nonorientable surfaces

Abstract

We prove that the n th pure braid group of a nonorientable surface (closed or with boundary, but different from RP2) is residually 2-finite. Consequently, this group is residually nilpotent. The key ingredient in the closed case is the notion of p-almost direct product, which is a generalization of the notion of almost direct product. We prove therefore also some results on lower central series and augmentation ideals of p-almost direct products.

References in corpus (4)

• A survey of surface braid groups and the lower algebraic K-theory of their group rings
• The braid groups of the projective plane and the Fadell-Neuwirth short exact sequence
• Exact sequences, lower central series and representations of surface braid groups
• Residual properties of automorphism groups of (relatively) hyperbolic groups

Cited by in corpus (5)

• Lower central series and split extensions
• When the lower central series stops: a comprehensive study for braid groups and their relatives
• The lower central and derived series of the braid groups of compact surfaces
• Lower central series, surface braid groups, surjections and permutations
• The pro-nilpotent Lawrence-Krammer-Bigelow representation