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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Decomposable braids as subgroups of braid groups


Author: H. Levinson
Journal: Trans. Amer. Math. Soc. 202 (1975), 51-55
MSC: Primary 55A25; Secondary 20F05
MathSciNet review: 0362287
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Abstract: The group of all decomposable $ 3$-braids is the commutator subgroup of the group $ {I_3}$ of all $ 3$-braids which leave strand positions invariant. The group of all $ 2$-decomposable $ 4$-braids is the commutator subgroup of $ {I_4}$, and the group of all decomposable $ 4$-braids is explicitly characterized as a subgroup of the second commutator subgroup of $ {I_4}$.


References [Enhancements On Off] (What's this?)

  • [1] E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101-126. MR 8, 367. MR 0019087 (8:367a)
  • [2] H. Levinson, Decomposable braids and linkages, Trans. Amer. Math. Soc. 178 (1973), 111-126. MR 0324684 (48:3034)
  • [3] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. Theorem 5.2, p. 290 and Equation 9, p. 290. MR 34 #7617. MR 0207802 (34:7617)

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DOI: https://doi.org/10.1090/S0002-9947-1975-0362287-3
Article copyright: © Copyright 1975 American Mathematical Society