Skip to main content
SpringerLink
Log in

Groupes finis simples sporadiques

  • Conference paper
  • First Online:

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Séminaire Bourbaki vol. 1969/70 Exposés 364–381

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 180))

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. FG = Theory of finite groups, A symposium, edited by R. BAUER and C.-S. SAH, Benjamin, New York, 1969.

    Google Scholar 

  2. E. ARTIN — The orders of the classical simple groups, Comm. P. Appl. Math., 8 (1955), 455–472.

    MATH  MathSciNet  Google Scholar 

  3. R. BRAUER — On the structure of groups of finite order, Proc. Int. Congr. Math. Amsterdam, 1954, vol. 1, 209–217.

    Google Scholar 

  4. R. BRAUER and P. FONG — A characterization of the Mathieu group M12, Trans. A. M. S., 122 (1966), 18–47.

    Article  MATH  MathSciNet  Google Scholar 

  5. N. BURGOYNE and P. FONG — The Schur multipliers of the Mathieu groups, Nagoya Math. J., 27 (1966), 733–745; 31 (1968), 297–304.

    MathSciNet  Google Scholar 

  6. R. CARTER — Simple groups and simple Lie algebras, J. Lond. Math. Soc., 40 (1965), 193–240.

    MATH  MathSciNet  Google Scholar 

  7. C. CHEVALLEY — Le groupe de Janko, Sém. Bourbaki, exp. 331, novembre 1967.

    Google Scholar 

  8. J. H. CONWAY — A group of order 8 315 553 613 086 720 000, Bull. Lond. Math. Soc., 1 (1969), 79–88. (Cf. aussi Proc. Nat. Acad. Sci. U. S. A., 61 (1968), 398–400.)

    MATH  MathSciNet  Google Scholar 

  9. J. H. CONWAY — A characterization of Leech's lattice, Inventiones Math., 7 (1969), 137–142.

    Article  MATH  MathSciNet  Google Scholar 

  10. B. FISCHER — Finite groups generated by 3-transpositions, Inventiones Math., à paraître.

    Google Scholar 

  11. T. M. GAGEN — A characterization of Janko's simple group, Proc. A. M. S., 19 (1968), 1393–1395.

    Article  MATH  MathSciNet  Google Scholar 

  12. M. HALL — The theory of groups, Macmillan, New York, 1959.

    MATH  Google Scholar 

  13. M. HALL and D. WALES — The simple group of order 604,800, J. Algebra, 9 (1968), 417–450. (Cf. aussi FG, 79–90.)

    Article  MATH  MathSciNet  Google Scholar 

  14. D. HELD — The simple group related to M24, J. Algebra, 13 (1969), 253–296. (Cf. aussi FG, 121–124.)

    Article  MATH  MathSciNet  Google Scholar 

  15. Donald G. HIGMAN — Finite permutation groups of rank 3, Math. Zeitschr., 86 (1964), 145–156.

    Article  MATH  MathSciNet  Google Scholar 

  16. D. G. HIGMAN and C. C. SIMS — A simple group of order 44,352,000, Math. Zeitschr., 105 (1968), 110–113.

    Article  MATH  MathSciNet  Google Scholar 

  17. Graham HIGMAN — On the simple group of D. G. Higman and C. C. Sims, Ill. Math. J., 13 (1969), 74–80.

    MATH  MathSciNet  Google Scholar 

  18. G. HIGMAN and J. McKAY — On Janko's simple group of order 50,232,960, Bull. Lond. Math. Soc., 1 (1969), 89–94. (Cf. aussi FG, 65–77.)

    MATH  MathSciNet  Google Scholar 

  19. Z. JANKO — A new finite simple group with abelian Sylow 2-subgroups and its characterization, J. Algebra, 3 (1966), 147–186. (Cf. aussi Proc. Nat. Acad. Sci. U. S. A., 53 (1965), 657–658.)

    Article  MATH  MathSciNet  Google Scholar 

  20. Z. JANKO — Some new simple groups of finite order, I, Ist. Naz. Alta Math., Symposia Mathematica, vol. I, Oderisi, Gubbio, 1968, 25–64. (Cf. aussi FG, 63–64.)

    Google Scholar 

  21. Z. JANKO — A characterization of the Mathieu groups, I, II, J. Algebra, 9 (1968), 1–19, 20–41.

    Article  MATH  MathSciNet  Google Scholar 

  22. Z. JANKO and S. K. WONG — A characterization of the Higman-Sims simple group, J. Algebra, 13 (1969), 517–534.

    Article  MATH  MathSciNet  Google Scholar 

  23. C. JORDAN — Traité des substitutions et des équations algébriques, Paris, Gauthier-Villars, 1870.

    MATH  Google Scholar 

  24. C. JORDAN — Recherches sur les substitutions, J. Math. P. Appl., (2) 17 (1872), 351–363.

    MATH  Google Scholar 

  25. G. KELLER — A characterization of A6 and M11, J. Algebra, 13 (1969), 409–421.

    Article  MATH  MathSciNet  Google Scholar 

  26. J. LEECH — Some sphere packings in higher space, Canadian J. Math., 16 (1964), 657–682.

    MATH  MathSciNet  Google Scholar 

  27. J. LEECH — Notes on sphere packings, Canadian J. Math., 19 (1967), 251–267.

    MATH  MathSciNet  Google Scholar 

  28. J. H. LINDSEY — Linear groups of degree 6 and the Hall-Janko group, FG, 97–100.

    Google Scholar 

  29. D. LIVINGSTONE — On a permutation representation of the Janko group, J. Algebra, 6 (1967), 43–55.

    Article  MATH  MathSciNet  Google Scholar 

  30. H. LÜNEBURG — Über die Gruppen von Mathieu, J. Algebra, 10 (1968), 194–210.

    Article  MATH  MathSciNet  Google Scholar 

  31. H. LÜNEBURG — Transitive Erweiterungen endlicher Permutationsgruppen, Lect. Notes Springer, no 84, 1969.

    Google Scholar 

  32. E. MATHIEU — Mémoire sur l'étude des fonctions de plusieurs quantités, J. Math. P. Appl., 6 (1861), 241–243.

    Google Scholar 

  33. E. MATHIEU — Sur les fonctions cinq fois transitives de 24 quantités, J. Math. P. Appl., 18 (1873), 25–46.

    MATH  Google Scholar 

  34. J. McLAUGHLIN — A simple group of order 898,128,000, FG, 109–111.

    Google Scholar 

  35. H. V. NIEMEYER — Definite quadratische Formen der Dimension 24 und Diskriminante 1, Thèse, Göttingen, 1968.

    Google Scholar 

  36. D. PARROTT and S. K. WONG — On the Higman-Sims simple group of order 44,352,000, Pacific J. Math., 32 (1970), 501–516.

    MATH  MathSciNet  Google Scholar 

  37. J. A. de SEGUIER — Eléments de la théorie des groupes de substitutions, Paris, Gauthier-Villars, 1912.

    MATH  Google Scholar 

  38. C. C. SIMS — On the isomorphism of two groups of order 44,352,000, FG, 101–108.

    Google Scholar 

  39. R. G. STANTON — The Mathieu groups, Canadian J. Math., 3 (1951), 164–174.

    MATH  MathSciNet  Google Scholar 

  40. M. SUZUKI — A simple group of order 448,345,497,600, FG, 113–119.

    Google Scholar 

  41. M. SUZUKI — Characterizations of linear groups, Bull. A. M. S., 75 (1969), 1043–1091.

    MATH  Google Scholar 

  42. J. G. THOMPSON — Characterizations of finite simple groups, Travaux Congr. Intern. Math. Moscou, 1966, 158–162.

    Google Scholar 

  43. J. G. THOMPSON — Nonsolvable finite groups all of whose local subgroups are solvable, Bull. A. M. S., 74 (1968), 383–437.

    MATH  Google Scholar 

  44. J. TITS — Généralisations des groupes projectifs basées sur leurs propriétés de transitivité, Acad. Roy. Belg. Mém. Cl. Sci., 27 (1952), fasc. 2.

    Google Scholar 

  45. J. TITS — Groupes simples et géométries associées, Proc. Intern. Congr. Math. Stockholm, 1962, 197–221.

    Google Scholar 

  46. J. TITS — Sur les systèmes de Steiner associés aux trois "grands" groupes de Mathieu, Rendiconti di Math., 25 (1964), 166–184.

    MathSciNet  Google Scholar 

  47. J. TITS — Le groupe de Janko d'ordre 604 800, FG, 91–95.

    Google Scholar 

  48. J. A. TODD — A representation of the Mathieu group M24 as a collineation group, Annali di Math., 71 (1966), 193–238.

    MathSciNet  Google Scholar 

  49. D. B. WALES — Generators of the Hall-Janko group as a subgroup of G2(4), J. Algebra, 13 (1969), 513–516.

    Article  MATH  MathSciNet  Google Scholar 

  50. D. B. WALES — The uniqueness of the simple group of order 604,800 as a subgroup of SL(6,4), J. Algebra, 11 (1969), 455–460.

    Article  MATH  MathSciNet  Google Scholar 

  51. E. WITT — Die 5-fach transitiven Gruppen von Mathieu, Abhandl. Math. Sem. Univ. Hamburg, 12 (1938), 256–265.

    MATH  Google Scholar 

  52. E. WITT — Über Steinersche Systeme, Abhandl. Math. Sem. Univ. Hamburg, 12 (1938), 265–274.

    MATH  Google Scholar 

  53. S. K. WONG — On a new finite non abelian simple group of Janko, à paraître.

    Google Scholar 

  54. H. ZASSENHAUS — Über transitive Erweiterungen gewisser Gruppen aus Automorphismen endlicher mehrdimensionaler Geometrien, Math. Ann., 111 (1938), 748–759.

    Article  MathSciNet  Google Scholar 

  55. N. BRYCE — Dissertation, Monash University, 1969

    Google Scholar 

  56. H. S. M. COXETER — Twelve points in PG(5,3) with 95040 self-transformations. Proc. Roy. Soc. London, Ser. A, 247 (1958), 279–293.

    Article  MATH  MathSciNet  Google Scholar 

  57. J. H. LINDSEY — On a projective representation of the Hall-Janko group, Bull. A. M. S., 74 (1968), 1094.

    Article  MATH  MathSciNet  Google Scholar 

  58. J. McKAY and D. WALES — The multipliers of the simple groups of order 604,800 and 50,232,960, à paraître.

    Google Scholar 

  59. D. PARROTT — On the Mathieu groups M22 and M11, J. Australian Math. Soc., 11 (1970), 69–81.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. Jacques Tits
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1971 N. Bourbaki

About this paper

Cite this paper

Tits, J. (1971). Groupes finis simples sporadiques. In: Séminaire Bourbaki vol. 1969/70 Exposés 364–381. Lecture Notes in Mathematics, vol 180. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0058832

Download citation

  • DOI: https://doi.org/10.1007/BFb0058832

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05357-6

  • Online ISBN: 978-3-540-36452-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation