Every two-generator knot is prime
HTML articles powered by AMS MathViewer
- by F. H. Norwood PDF
- Proc. Amer. Math. Soc. 86 (1982), 143-147 Request permission
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
- B. H. Neumann, On the number of generators of a free product, J. London Math. Soc. 18 (1943), 12–20. MR 8809, DOI 10.1112/jlms/s1-18.1.12 F. H. Norwood, One-relator knots, Dissertation, Univ. Southwestern Louisiana, 1979.
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, No. 7, Publish or Perish, Inc., Berkeley, Calif., 1976. MR 0515288
- Joseph J. Rotman, The theory of groups. An introduction, Allyn and Bacon, Inc., Boston, Mass., 1965. MR 0204499
- Jonathan Simon, Roots and centralizers of peripheral elements in knot groups, Math. Ann. 222 (1976), no. 3, 205–209. MR 418079, DOI 10.1007/BF01362577
- John R. Stallings, A topological proof of Grushko’s theorem on free products, Math. Z. 90 (1965), 1–8. MR 188284, DOI 10.1007/BF01112046
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 143-147
- MSC: Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1982-0663884-7
- MathSciNet review: 663884