Israel Journal of Mathematics

, Volume 82, Issue 1–3, pp 341–362 | Cite as

The last flag-transitiveP-geometry

  • A. A. Ivanov
  • S. V. Shpectorov


The universal 2-cover of theP-geometry related to the Baby Monster sporadic simple groupBM is shown to admit a non-split extension 34371·BM as a flag-transitive automorphism group. This new geometry completes the list of flag-transitiveP-geometries.


Automorphism Group Conjugacy Class Maximal Subgroup Parabolic Subgroup Outer Automorphism 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Aschbacher,Flag structures on Tits geometries, Geom. Dedic.14 (1983), 21–32.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    K.S. Brown,Cohomology of groups, Springer Verlag, Berlin, 1982.MATHGoogle Scholar
  3. [3]
    F. Buekenhout,Diagrams for geometries and groups, J. Comb. TheoryA27 (1979), 121–151.CrossRefMathSciNetGoogle Scholar
  4. [4]
    J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson,Atlas of Finite Groups, Clarendon Press, Oxford, 1985.MATHGoogle Scholar
  5. [5]
    C. Curtis and I. Reiner,Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons Inc., New York, 1988.MATHGoogle Scholar
  6. [6]
    D.G. Higman,A monomial character of Fischer’s Baby Monster, inProc. of the Conference on Finite Groups (W.R. Scott and F. Gross, eds.), Academic Press, New York, 1976.Google Scholar
  7. [7]
    A.A. Ivanov,On 2-transitive graphs of girth 5, Eur. J. Comb.8 (1987), 393–420.MATHGoogle Scholar
  8. [8]
    A.A. Ivanov,A geometric characterization of Fischer’s Baby Monster, J. Alg. Comb.1 (1992), 45–69.MATHCrossRefGoogle Scholar
  9. [9]
    A.A. Ivanov and S.V. Shpectorov,Geometries for sporadic groups related to the Petersen graph. II, Eur. J. Comb.10 (1989), 347–361.MATHMathSciNetGoogle Scholar
  10. [10]
    A.A.Ivanov and S.V.Shpectorov,An infinite family of simply connected flag-transitive tilde geometries, Geom. Dedic., to appear.Google Scholar
  11. [11]
    A.A.Ivanov and S.V.Shpectorov,Natural representations of the P-geometries of Co 2-type, J. Algebra, to appear.Google Scholar
  12. [12]
    R.A.Parker,A collection of modular characters, preprint, Univ. of Cambridge, 1989.Google Scholar
  13. [13]
    M.A. Ronan and S.D. Smith,Universal presheaves on group geometries, and modular representations, J. Algebra102 (1986), 135–154.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    S.V. Shpectorov,A geometric characterization of the group M 22, inInvestigations in the Algebraic Theory of Combinatorial Objects, Moscow, VNIISI, 1985, pp. 112–123 (in Russian).Google Scholar
  15. [15]
    S.V. Shpectorov,The universal 2-cover of the P-geometry \({\mathcal{G}}\)(Co 2), Eur. J. Comb.13 (1992), 291–312.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    R.A. Wilson,The maximal subgroups of Conway’s group.2, J. Algebra84 (1983), 107–114.MATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    R.A. Wilson,The action of a maximal parabolic subgroup on the transpositions of the Baby Monster, preprint, 1992.Google Scholar

Copyright information

© Hebrew University 1993

Authors and Affiliations

  • A. A. Ivanov
    • 1
  • S. V. Shpectorov
    • 1
  1. 1.Institute for System AnalysisRussian Academy of SciencesMoscowRussia

Personalised recommendations