The commutator subgroup of the braid group is generated by two elements
Geometric Topology
2020-03-11 v2 Group Theory
Abstract
For at least 7 and equal to 5, we give generating sets of size 2 for the commutator subgroup of the braid group on strands. These generating sets are of the smallest possible cardinality. For 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.
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