Skip to main content

Artin groups and infinite Coxeter groups

This is a preview of subscription content, access via your institution.


  1. Birman, J.: Braids, Links, and Mapping Class Groups. Princeton, N.J.: Princeton University Press 1974

    Google Scholar 

  2. Bourbaki, N.: Groupes et algèbres de Lie, Chapitres 4, 5, et 6, Eléments de Mathématique XXXIV. Paris: Hermann 1968

    Google Scholar 

  3. Brieskorn, E.: Die Fundamentalgruppe des Raumes der Regulären Orbits einer endlichen komplexen Spielsgruppe. Invent. Math.12, 57–61 (1971)

    Google Scholar 

  4. Brieskorn, E., Saito, K.: Artin-gruppen und Coxeter-gruppen. Invent. Math.17, 245–271 (1972)

    Google Scholar 

  5. Coxeter, H.S.M.: The complete enumeration of finite groups of the formR 2i =(R iRj)k ij=1. J. London Math. Soc.10, 21–25 (1935)

    Google Scholar 

  6. Deligne, P.: Les immeubles des groupes de tresses généralisés. Invent. Math.17, 273–302 (1972)

    Google Scholar 

  7. Garside, F.A.: The braid group and other groups. Quart. J. Math. Oxford, 2 Ser.20, 235–254 (1969)

    Google Scholar 

  8. Len, V.Y.: Artin's braids and their connections with groups and spaces. Etoge Nauke e Texneke. Algebra, Topologeya, Geometreya, Tom 17

  9. Lyndon, R.C.: On Dehn's algorithm. Math. Ann.166, 208–228 (1966)

    Google Scholar 

  10. Lyndon, R.C., Schupp, P.E.: Combinatorial Group Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. Berlin: Springer 1977

    Google Scholar 

  11. Schupp, P.E.: A survey of small cancellation theory. Word Problems, pp. 569–589. Amsterdam: North Holland 1973

    Google Scholar 

  12. Tits, J.: Le problème des mots dans les groupes de Coxeter. Instituto Nazionale di Alta Mathematica, Symposia Mathematica 1, 175–185 (1968)

    Google Scholar 

  13. Tits, J.: Normalisateurs de tores I. Groupes de Coxeter étendus. J. Algebra 4, 96–116 (1966)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Additional information

This work was supported by NSF grants MCS 7902512 and MCS 7703452. The authors would like to thank the referee for an extremely careful reading of the paper and many helpful suggestions

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Appel, K.I., Schupp, P.E. Artin groups and infinite Coxeter groups. Invent Math 72, 201–220 (1983).

Download citation

  • Issue Date:

  • DOI:


  • Coxeter Group
  • Artin Group
  • Infinite Coxeter Group