Abstract
The group-admissible embeddings of flag-transitive classical locally polar geometries of rank 3 are determined, as well as those of truncations of the related dual polar spaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Conway, J. H. et al., Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
Brouwer, A., Cohen, A. and Neumaier, A., Distance-Regular Graphs, Ser. Modern Surveys in Math. 18, Springer, New York, 1989.
Benson, D., ‘Modular representation theory: New trends and methods’, Lecture Notes in Math. 1081, Springer, New York, 1984.
Buekenhout, F. and Hubout, X., ‘Locally polar spaces and related rank 3 groups’, J. Algebra 45 (1977), 391–434.
Buekenhout, F. and Lefèvre, C., ‘Generalized quadrangles in projective spaces’, Arch. Math. 25 (1974), 540–552.
Bagchi, B. and Sastry, S., ‘Codes associated with generalized polygons’, Geom. Dedicata 27 (1988), 1–8.
Buekenhout, F., ‘Diagram geometries for the sporadic groups’, in Finite Groups: Coming of Age. Contemporary Math. 45, Providence RI, Amer. Math. Soc., 1985, pp. 1–32.
Conway, J. H., ‘Three lectures on exceptional groups’, in Finite Simple Groups (eds M. B. Powell and G. Higman), Academic Press, 1971, pp. 215–247.
Conway, J. H. and Sloane, N. J. A., ‘The Coxeter-Todd lattice, the Mitchell group, and related sphere packings’, Math. Proc. Camb. Phil. Soc. 93 (1983), 421–440.
Curtis, R. T., ‘On subgroups of 0, I Lattice stabilizers’, J. Algebra 27 (1973), 549–573.
Del Fra, A., Ghinelli, D., Meixner, T. and Pasini, A., ‘Flag-transitive extensions of C n -geometries’, Geom. Dedicata 37 (1991), 253–273.
Ivanov, A. A. and Shpectorov, S. V., ‘Universal representations of P-geometries from F 2-series’ (to appear in J. Algebra).
Kleidman, P. and Liebeck, M., The Subgroup Structure of the Finite Classical Groups. London Math. Soc. Lecture Notes 129, Cambridge Univ. Press, Cambridge, 1990.
Lindsey, J. H. Jr., ‘A correlation between PSU4(3), the Suzuki group, and the Conway group’, Trans. Amer. Math. Soc. 157 (1971), 189–204.
Pasini, A., ‘A classification of a class of Buekenhout geometries exploiting amalgams and simple connectedness’, (to appear in Atti Sem. Mat. Fis. Univ. Modena).
Pasini, A., ‘Quotients of affine polar spaces’, (to appear in Bull. Soc. Math. Belgique).
Payne, S. and Thas, J., Finite Generalized Quadrangles. Research Notes in Math. 110, Pitman, Boston, 1984.
Pasini, A. and Yoshiara, S., ‘Flag-transitive Buekenhout geometries’ (to appear in the Proceedings of the Conference Combinatorics 90, held in Gaeta, 1990).
Ronan, M., ‘Embedding and hyperplanes of discrete geometries’, European J. Combin. 8 (1987), 179–185.
Ronan, M. and Stroth, G., ‘Minimal parabolic geometries for the sporadic groups’, European J. Combin. 5 (1984), 59–91.
Ronan, M. and Smith, S. D., ‘2-local geometries for some sporadic simple groups’, in The Santa Cruz Conference on Finite Groups (eds B. Cooperstein and G. Mason), Proc. Symp. Pure Math. 37, Amer. Math. Soc., Providence, RI, 1980, pp. 283–289.
Smith, S. D., ‘Geometric methods in group theory’, in Algebraic, Extremal, and Metric Combinatorics, 1986 (eds Deza, Frankl and Rosenberg), Cambridge Univ. Press, 1988, pp. 219–237.
Wilson, R. A., ‘The complex Leech lattice and maximal subgroups of the Suzuki group’, J. Algebra 84 (1983), 151–188.
Weiss, R. and Yoshiara, S., ‘A geometric characterization of the groups HS and Suz’, J. Algebra 133 (1990), 182–196.
Yoshiara, S., ‘A locally polar geometry associated with the group HS’, European J. Combin. 11 (1990), 81–93.
Yoshiara, S., ‘Ternary, quarternary Golay codes and complex, quarternionic Leech lattices’, Reports of research on group theory and its applications (in Japanese), 1983.
Yoshiara, S., ‘A classification of flag-transitive classical c. C 2-geometries by means of generators and relations’, European J. Combin. 12 (1991), 159–181.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yoshiara, S. Embeddings of flag-transitive classical locally polar geometries of rank 3. Geom Dedicata 43, 121–165 (1992). https://doi.org/10.1007/BF00147865
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00147865