Finite simple groups and their subgroups

  • Michael Aschbacher
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1185)


Finite Group Simple Group Maximal Subgroup Finite Simple Group Permutation Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Aschbacher, M., The classification of the finite simple groups, Math. Intelligencer. 3 (1981), 59–65.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Aschbacher, M., A characterization of Chevalley groups over fields of odd order, Ann. Math., 106 (1977), 353–468.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Aschbacher, M., Finite groups generated by odd transpositions, I, II, III, IV, Math. Z., 127 (1972), 45–56, J.Alg. 26 (1973), 451–491.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Aschbacher, M., On the maximal subgroups of the finite classical groups, Invent. Math., 76 (1984), 469–514.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Aschbacher, M. and Scott, L., Maximal subgroups of finite groups, J. Alg. 92 (1985), 44–80.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Aschbacher, M., The Finite Simple Groups and their Classification, Yale University Press, New Haven, 1980.MATHGoogle Scholar
  7. 7.
    Aschbacher, M., A homomorphism theorem for finite graphs, Proc. AMS, 54 (1976), 468–470.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Aschbacher, M., Finite geometries of type C3 with flag transitive groups, Geom. Ded., 16 (1984), 195–200.CrossRefMATHGoogle Scholar
  9. 9.
    Aschbacher, M., Flag structures on Tits geometries, Geom. Ded., 14 (1983), 21–32.MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Aschbacher, M., and Smith, S., Tits geometries over GF(2) defined by groups over GF(3), Comm. Alg., 11 (1983), 1675–1684.MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Borel, A. et al, Seminar on Algebraic Groups and Related Finite Groups, Springer-Verlag, Berlin, 1970.CrossRefGoogle Scholar
  12. 12.
    Borel, A. and Tits, J., Elements unipotents et sousgroupes paraboliques de groupes reductifs, Invent. Math., 12 (1971), 97–104.CrossRefMATHGoogle Scholar
  13. 13.
    Cooperstein, B., Subgroups of exceptional groups of Lie type generated by long root elements, I; Odd characteritic, J. Alg., 70 (1981), 270–282.MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Cooperstein, B., The geometry of root subgroups in exceptional groups, I, Geom. Ded., 8 (1979), 317–381.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Enright, G., Subgroups generated by transpositions in F22 and F23, Comm. Alg., 6 (1978), 823–837.CrossRefMATHGoogle Scholar
  16. 16.
    Fischer, B., Finite groups generated by 3-transpositions, University of Warwick preprint.Google Scholar
  17. 17.
    Gorenstein, D., The Classification of Finite Simple Groups, I, Plenum Press, New York, 1983.CrossRefMATHGoogle Scholar
  18. 18.
    Gorenstein, D., Finite Simple Groups; An Introduction to their Classification, Plenum Press, New York, 1982.MATHGoogle Scholar
  19. 19.
    Gross, F., and Kovacs, L., Maximal subgroups in composite finite groups, to appear.Google Scholar
  20. 20.
    Ho, C., On the quadratic pairs, J. Alg., 43 (1976), 338–358.MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Kantor, W., Subgroups of classical groups generated by long root elements, Trans. AMS, 248 (1979), 347–379.MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Kantor, W., Primitive permutation groups of odd degree, and an application to finite projective planes, to appear.Google Scholar
  23. 23.
    Niles, R., Finite groups with parabolic type subgroups must have a BN-pair, J. Alg., 75 (1982), 484–494.MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Seitz, G., The root subgroups for maximal tori in finite groups of Lie type, to appear.Google Scholar
  25. 25.
    Seitz, G., Flag transitive subgroups of Chevalley groups, Ann. Math., 97 (1974), 27–56.MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Stark, B., Another look at Thompson's quadratic pairs, J. Alg. 45 (1977), 334–342.MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Timmesfeld, F., Tits geometries and parabolic systems of rank 3, to appear.Google Scholar
  28. 28.
    Timmesfeld, F., Tits geometries and parabolic systems in finite groups, to appear.Google Scholar
  29. 29.
    Timmesfeld, F., Groups generated by root involutions, I, II, J. Alg., 33 (1975), 75–134.MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Tits, J., A local approach to buildings, The Geometric Vein, 517–547, Springer., 1981.Google Scholar
  31. 31.
    Tits, J., Buildings of Spherical Type and Finite (B,N)-Pairs, Springer-Verlag, Berlin, 1974.MATHGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Michael Aschbacher
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

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