English

The commutator subgroup of the braid group is generated by two elements

Geometric Topology 2020-03-11 v2 Group Theory

Abstract

For nn at least 7 and nn equal to 5, we give generating sets of size 2 for the commutator subgroup of the braid group on nn strands. These generating sets are of the smallest possible cardinality. For nn equal to 4 or 6, we give generating sets of size three. We also prove that the commutator subgroup of the braid group on 4 strands cannot be generated by fewer than three elements.

Keywords

Cite

@article{arxiv.1910.06944,
  title  = {The commutator subgroup of the braid group is generated by two elements},
  author = {Kevin Kordek},
  journal= {arXiv preprint arXiv:1910.06944},
  year   = {2020}
}

Comments

8 pages, 1 figure; final version; to appear in Proc. Amer. Math. Soc

R2 v1 2026-06-23T11:44:35.505Z