Martin David Palmer -- Preprint -- When the lower central series stops
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When the lower central series stops
with Jacques Darné and Arthur Soulié
(v1: 2022, v2: 2022)

arXiv: abspdf
v2v1

Abstract

Our aim here is to showcase several techniques for studying the lower central series of a group and, in particular, for determining whether or not it stops. We apply these techniques to various groups related to braid groups, in particular Artin groups, surface braid groups, groups of welded and virtual braids and partitioned versions of all of these groups.

GAP code

We made some conjectures in the article about the few remaining unknown (or known-only-up-to-an-ambiguity) cases. These were based on experimental calculations of lower central series of certain finitely-presented groups using GAP and the NQ package. The code used for these is below (and also available here):

  • For the (1,m)-th partitioned braid groups on the projective plane – B1mP.g
  • For the (2,m)-th partitioned braid groups on the projective plane – B2mP.g
  • For the (2,m)-th partitioned braid groups on the sphere – B2mS.g