The commutator subgroup of the braid group is generated by two elements
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- by Kevin Kordek;
- Proc. Amer. Math. Soc. 151 (2023), 2741-2748
- DOI: https://doi.org/10.1090/proc/15091
- Published electronically: April 6, 2023
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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.References
- R. Inanc Baykur and Mustafa Korkmaz, The mapping class group is generated by two commutators, arXiv:1908.11306, 2019.
- Lei Chen, Kevin Kordek, and Dan Margalit, Homomorphisms between braid groups, arXiv:1910.00712, 2019.
- E. A. Gorin and V. Ja. Lin, Algebraic equations with continuous coefficients, and certain questions of the algebraic theory of braids, Mat. Sb. (N.S.) 78(120) (1969), 579–610 (Russian). MR 251712
- Vladimir Lin, Braids and permutations, arXiv:math/0404528, 2004.
Bibliographic Information
- Kevin Kordek
- Affiliation: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332
- MR Author ID: 1202384
- Email: kevin.a.kordek@gmail.com
- Received by editor(s): October 17, 2019
- Received by editor(s) in revised form: February 20, 2020
- Published electronically: April 6, 2023
- Additional Notes: The author was supported by National Science Foundation Grant No. DMS - 1057874.
- Communicated by: Kenneth Bromberg
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 2741-2748
- MSC (2020): Primary 20F36; Secondary 57M07, 20F05
- DOI: https://doi.org/10.1090/proc/15091
- MathSciNet review: 4579352