2020•Proceedings of the American Mathematical SocietyOpen access
The commutator subgroup of the braid group is generated by two elements
Kevin Kordek
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Abstract
For n n at least 7 and n n equal to 5, we give generating sets of size 2 for the commutator subgroup of the braid group on n n strands. These generating sets are of the smallest possible cardinality. For n 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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