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Groupes finis simples sporadiques

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

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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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.)

    CrossRef  MATH  MathSciNet  Google Scholar 

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

    CrossRef  MATH  MathSciNet  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.)

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  MATH  MathSciNet  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  MATH  MathSciNet  Google Scholar 

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

    CrossRef  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.

    CrossRef  MATH  MathSciNet  Google Scholar 

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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

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