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

MSC:
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
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References:
[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
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