Skip to main content
Log in

On Dehn's algorithm

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  1. Berge, C.: Théorie des graphes et ses applications. Paris: Dunod 1958.

    Google Scholar 

  2. Boone, W. W.: Review ofBritton [3]. Math. Reviews23, 440–441 (1962), A 2325.

    Google Scholar 

  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. 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. Dehn, M.: Über unendliche diskontinuierliche Gruppen. Math. Ann.71, 116–144 (1912).

    Google Scholar 

  6. —— Transformation der Kurven auf zweiseitigen Flächen. Math. Ann.72, 413–421 (1912).

    Google Scholar 

  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. Gladkii, A. V.: On simple Dyck words. Sibirsk Mat. Zh.2, 36–45 (1961).

    Google Scholar 

  9. Greendlinger, M.: Dehn's algorithm for the word problem. Comm. Pure Appl. Math.13, 67–83 (1960).

    Google Scholar 

  10. —— On Dehn's algorithms for the conjugacy and word problems with applications. Comm. Pure Appl. Math.13, 641–677 (1960).

    Google Scholar 

  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. —— 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. Levin, F.: Solutions of equations over groups. Bull. Am. Math. Soc.68, 603–604 (1962).

    Google Scholar 

  14. Lipschutz, S.: Elements inS-groups with trivial centralizers. Comm. Pure Appl. Math.13, 679–683 (1960).

    Google Scholar 

  15. Lyndon, R. C.: Cohomology theory of groups with a single defining relation. Ann. of Math.52, 650–665 (1950).

    Google Scholar 

  16. —— Dependence and independence in free groups. Crelles J.210, 148–174 (1962).

    Google Scholar 

  17. Reidemeister, K.: Einführung in die kombinatorische Topologie. Braunschweig: Vieweg 1932.

    Google Scholar 

  18. Schiek, H.: Ähnlichkeitsanalyse von Gruppenrelationen. acta Math.96, 157–251 (1956).

    Google Scholar 

  19. —— Das Adjunktionsproblem der Gruppentheorie. Math. Ann.147, 159–165 (1962).

    Google Scholar 

  20. Tartakovskii, V. A.: The sieve method in group theory. Mat. Sbornik (N.S.)25, (67), 3–50 (1949).

    Google Scholar 

  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. —— 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. —— On primitive composition. Mat. Sbornik (N.S.)30, (72), 39–52 (1952).

    Google Scholar 

  24. -- Translations of [20, 21, 22]. Am. Math. Soc. Translations60 (1952), reprint1 (1962).

  25. Zieschang, H.: Studien zur kombinatorischen Topologie von Flächen und ebenen diskontinuierlichen Gruppen (multigraphed). Frankfurt 1964 (priv. Veröffentlichung).

Additional bibliography

  1. Blanc, C.: Une interprétation élémentaire des théorèmes fondamentaux de M. Nevanlinna. Comm. Math. Helv.12, 153–163 (1940).

    Google Scholar 

  2. —— Les résaux Riemanniens. Comm. Math. Helv.13, 54–67 (1941).

    Google Scholar 

  3. Fiala, F.: Sur les polyèdres à faces triangulaires. Comm. Math. Helv.19, 83–90 (1946).

    Google Scholar 

  4. Gladkii, A. V.: On groups withk-reducible bases. Dokl. Akad. Nauk SSSR134, 16–18 (1960).

    Google Scholar 

  5. —— On groups withk-reducible bases. Sibirsk Math. J.2, 366–383 (1961).

    Google Scholar 

  6. Orlik, P. P. N.: Necessary conditions for the homeomorphism of Seifert-manifolds. Thesis, University of Michigan, 1966.

  7. Schupp, P. E.: On Dehn's algorithm and the conjugacy problem. Thesis, University of Michigan, 1966. (To be submitted to Math. Ann.)

  8. van Kampen, E. R.: One some lemmas in the theory of groups. Ann. J. Math.55, 268–273 (1933).

    Google Scholar 

  9. Weinbaum, C. M.: Visualizing the word problem, with an application to sixth groups. Pacific J. Math.16, 557–578 (1966).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

I wish to acknowledge the hospitality of Queen Mary College, London, where this work was done, and also the support of the National Science Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lyndon, R.C. On Dehn's algorithm. Math. Ann. 166, 208–228 (1966). https://doi.org/10.1007/BF01361168

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01361168

Navigation