Abstract
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.
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References
M. Aschbacher,Flag structures on Tits geometries, Geom. Dedic.14 (1983), 21–32.
K.S. Brown,Cohomology of groups, Springer Verlag, Berlin, 1982.
F. Buekenhout,Diagrams for geometries and groups, J. Comb. TheoryA27 (1979), 121–151.
J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson,Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
C. Curtis and I. Reiner,Representation Theory of Finite Groups and Associative Algebras, John Wiley & Sons Inc., New York, 1988.
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.
A.A. Ivanov,On 2-transitive graphs of girth 5, Eur. J. Comb.8 (1987), 393–420.
A.A. Ivanov,A geometric characterization of Fischer’s Baby Monster, J. Alg. Comb.1 (1992), 45–69.
A.A. Ivanov and S.V. Shpectorov,Geometries for sporadic groups related to the Petersen graph. II, Eur. J. Comb.10 (1989), 347–361.
A.A.Ivanov and S.V.Shpectorov,An infinite family of simply connected flag-transitive tilde geometries, Geom. Dedic., to appear.
A.A.Ivanov and S.V.Shpectorov,Natural representations of the P-geometries of Co 2-type, J. Algebra, to appear.
R.A.Parker,A collection of modular characters, preprint, Univ. of Cambridge, 1989.
M.A. Ronan and S.D. Smith,Universal presheaves on group geometries, and modular representations, J. Algebra102 (1986), 135–154.
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).
S.V. Shpectorov,The universal 2-cover of the P-geometry \({\mathcal{G}}\)(Co 2), Eur. J. Comb.13 (1992), 291–312.
R.A. Wilson,The maximal subgroups of Conway’s group.2, J. Algebra84 (1983), 107–114.
R.A. Wilson,The action of a maximal parabolic subgroup on the transpositions of the Baby Monster, preprint, 1992.
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Dedicated to Prof. J. Thompson
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Ivanov, A.A., Shpectorov, S.V. The last flag-transitiveP-geometry. Israel J. Math. 82, 341–362 (1993). https://doi.org/10.1007/BF02808117
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DOI: https://doi.org/10.1007/BF02808117