zbMATH — the first resource for mathematics

Every two-generator knot is prime. (English) Zbl 0506.57004

57M25 Knots and links in the \(3\)-sphere (MSC2010)
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
Full Text: DOI
[1] B. H. Neumann, On the number of generators of a free product, J. London Math. Soc. 18 (1943), 12 – 20. · Zbl 0028.33901 · doi:10.1112/jlms/s1-18.1.12 · doi.org
[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. · Zbl 0339.55004
[4] Joseph J. Rotman, The theory of groups. An introduction, Allyn and Bacon, Inc., Boston, Mass., 1965. · Zbl 0123.02001
[5] Jonathan Simon, Roots and centralizers of peripheral elements in knot groups, Math. Ann. 222 (1976), no. 3, 205 – 209. · Zbl 0314.55003 · doi:10.1007/BF01362577 · doi.org
[6] John R. Stallings, A topological proof of Grushko’s theorem on free products, Math. Z. 90 (1965), 1 – 8. · Zbl 0135.04603 · doi:10.1007/BF01112046 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.