Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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
  • [2] F. H. Norwood, One-relator knots, Dissertation, Univ. Southwestern Louisiana, 1979.
  • [3] Dale Rolfsen, Knots and links, Publish or Perish, Inc., Berkeley, Calif., 1976. Mathematics Lecture Series, No. 7. MR 0515288
  • [4] Joseph J. Rotman, The theory of groups. An introduction, Allyn and Bacon, Inc., Boston, Mass., 1965. MR 0204499
  • [5] Jonathan Simon, Roots and centralizers of peripheral elements in knot groups, Math. Ann. 222 (1976), no. 3, 205–209. MR 0418079
  • [6] John R. Stallings, A topological proof of Grushko’s theorem on free products, Math. Z. 90 (1965), 1–8. MR 0188284

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57M25

Retrieve articles in all journals with MSC: 57M25

Additional Information

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