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

Kevin Kordek

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arXiv · 1910.06944

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

Kevin Kordek

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Abstract

For $n$ at least 7 and $n$ equal to 5, we give generating sets of size 2 for the commutator subgroup of the braid group on $n$ strands. These generating sets are of the smallest possible cardinality. For $n$ 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.

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Kevin Kordek. 2019-10-15. The commutator subgroup of the braid group is generated by two elements. https://arxiv.org/abs/1910.06944

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