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Mathematische Annalen

, Volume 166, Issue 3, pp 208–228 | Cite as

On Dehn's algorithm

  • Roger C. Lyndon
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Bibliography

  1. [1]
    Berge, C.: Théorie des graphes et ses applications. Paris: Dunod 1958.Google Scholar
  2. [2]
    Boone, W. W.: Review ofBritton [3]. Math. Reviews23, 440–441 (1962), A 2325.Google Scholar
  3. [3]
    Britton, J. L.: Solution of the word problem for certain types of groups, I, II. Proc. Glasgow Math. Ass.3, 45–54, 68–90 (1956–58).Google Scholar
  4. [4]
    Cohen, D. E., andR. C. Lyndon: Free bases for normal subgroups of free groups. Trans. Am. Math. Soc.108, 528–537 (1963).Google Scholar
  5. [5]
    Dehn, M.: Über unendliche diskontinuierliche Gruppen. Math. Ann.71, 116–144 (1912).Google Scholar
  6. [6]
    —— Transformation der Kurven auf zweiseitigen Flächen. Math. Ann.72, 413–421 (1912).Google Scholar
  7. [7]
    Gerstenhaber, M., andO. S. Rothaus: The solution of sets of equations in groups. Proc. Nat. Acad. Sci. U.S.48, 1531–1533 (1962).Google Scholar
  8. [8]
    Gladkii, A. V.: On simple Dyck words. Sibirsk Mat. Zh.2, 36–45 (1961).Google Scholar
  9. [9]
    Greendlinger, M.: Dehn's algorithm for the word problem. Comm. Pure Appl. Math.13, 67–83 (1960).Google Scholar
  10. [10]
    —— On Dehn's algorithms for the conjugacy and word problems with applications. Comm. Pure Appl. Math.13, 641–677 (1960).Google Scholar
  11. [11]
    —— Solutions of the word problem for a class of groups by means of Dehn's algorithm, and of the conjugacy problem by means of a generalization of Dehn's algorithm. Dokl. Akad. Nauk SSSR154, 507–509 (1964).Google Scholar
  12. [12]
    —— Solution of the conjugacy problem for a class of groups coinciding with their anti-centers, by means of the generalized Dehn algorithm. Dokl. Akad. Nauk SSSR158, 1254–1256 (1964).Google Scholar
  13. [13]
    Levin, F.: Solutions of equations over groups. Bull. Am. Math. Soc.68, 603–604 (1962).Google Scholar
  14. [14]
    Lipschutz, S.: Elements inS-groups with trivial centralizers. Comm. Pure Appl. Math.13, 679–683 (1960).Google Scholar
  15. [15]
    Lyndon, R. C.: Cohomology theory of groups with a single defining relation. Ann. of Math.52, 650–665 (1950).Google Scholar
  16. [16]
    —— Dependence and independence in free groups. Crelles J.210, 148–174 (1962).Google Scholar
  17. [17]
    Reidemeister, K.: Einführung in die kombinatorische Topologie. Braunschweig: Vieweg 1932.Google Scholar
  18. [18]
    Schiek, H.: Ähnlichkeitsanalyse von Gruppenrelationen. acta Math.96, 157–251 (1956).Google Scholar
  19. [19]
    —— Das Adjunktionsproblem der Gruppentheorie. Math. Ann.147, 159–165 (1962).Google Scholar
  20. [20]
    Tartakovskii, V. A.: The sieve method in group theory. Mat. Sbornik (N.S.)25, (67), 3–50 (1949).Google Scholar
  21. [21]
    —— Application of the sieve method to the solution of the word problem for certain types of groups. Mat. Sbornik (N.S.)25, (67), 251–274 (1949).Google Scholar
  22. [22]
    —— Solution of the word problem for groups with ak-reduced basis fork>6. Izvestiya Akad. Nauk SSSR, Ser. Mat.13, 483–494 (1949).Google Scholar
  23. [23]
    —— On primitive composition. Mat. Sbornik (N.S.)30, (72), 39–52 (1952).Google Scholar
  24. [24]
    -- Translations of [20, 21, 22]. Am. Math. Soc. Translations60 (1952), reprint1 (1962).Google Scholar
  25. [25]
    Zieschang, H.: Studien zur kombinatorischen Topologie von Flächen und ebenen diskontinuierlichen Gruppen (multigraphed). Frankfurt 1964 (priv. Veröffentlichung).Google Scholar

Additional bibliography

  1. [26]
    Blanc, C.: Une interprétation élémentaire des théorèmes fondamentaux de M. Nevanlinna. Comm. Math. Helv.12, 153–163 (1940).Google Scholar
  2. [27]
    —— Les résaux Riemanniens. Comm. Math. Helv.13, 54–67 (1941).Google Scholar
  3. [28]
    Fiala, F.: Sur les polyèdres à faces triangulaires. Comm. Math. Helv.19, 83–90 (1946).Google Scholar
  4. [29]
    Gladkii, A. V.: On groups withk-reducible bases. Dokl. Akad. Nauk SSSR134, 16–18 (1960).Google Scholar
  5. [30]
    —— On groups withk-reducible bases. Sibirsk Math. J.2, 366–383 (1961).Google Scholar
  6. [31]
    Orlik, P. P. N.: Necessary conditions for the homeomorphism of Seifert-manifolds. Thesis, University of Michigan, 1966.Google Scholar
  7. [32]
    Schupp, P. E.: On Dehn's algorithm and the conjugacy problem. Thesis, University of Michigan, 1966. (To be submitted to Math. Ann.)Google Scholar
  8. [33]
    van Kampen, E. R.: One some lemmas in the theory of groups. Ann. J. Math.55, 268–273 (1933).Google Scholar
  9. [34]
    Weinbaum, C. M.: Visualizing the word problem, with an application to sixth groups. Pacific J. Math.16, 557–578 (1966).Google Scholar

Copyright information

© Springer-Verlag 1966

Authors and Affiliations

  • Roger C. Lyndon
    • 1
  1. 1.Department of MathematicsThe University of MichiganAnn ArborUSA

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