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

Paolo Bellingeri; Sylvain Gervais

doi:10.2140/agt.2016.16.547

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arXiv · 1412.0186

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

Paolo Bellingeri·Sylvain Gervais

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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.

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Paolo Bellingeri, Sylvain Gervais. 2014-11-30. On p-almost direct products and residual properties of pure braid groups of nonorientable surfaces. https://doi.org/10.2140/agt.2016.16.547

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