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Every two-generator knot is prime

Author: F. H. Norwood
Journal: Proc. Amer. Math. Soc. 86 (1982), 143-147
MSC: Primary 57M25
MathSciNet review: 663884
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Abstract: Theorem. Every two-generator knot is prime. The proof gives conditions under which a free product with amalgamation cannot be generated by two elements. An example is given of a composite one-relator link.

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

  • [1] B. H. Neumann, On the number of generators of a free product, J. London Math. Soc. 18 (1943), 12-20. MR 0008809 (5:58t)
  • [2] F. H. Norwood, One-relator knots, Dissertation, Univ. Southwestern Louisiana, 1979.
  • [3] D. Rolfsen, Knots and links, Math. Lectures, vol. 7, Publish or Perish, Berkeley, Calif., 1976. MR 0515288 (58:24236)
  • [4] J. J. Rotman, The theory of groups: An introduction, Allyn and Bacon, Boston, Mass., 1965. MR 0204499 (34:4338)
  • [5] J. Simon, Roots and centralizers of peripheral elements in knot groups, Math. Ann. 222 (1976), 205-209. MR 0418079 (54:6123)
  • [6] J. Stallings, A topological proof of Grushko's theorem on free products, Math. Z. 90 (1965), 1-8. MR 0188284 (32:5723)

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Keywords: One-relator knot, free product with amalgamation
Article copyright: © Copyright 1982 American Mathematical Society

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