A geometric characterization of the groups M12, He and Ru

Richard WEISS

doi:10.2969/jmsj/04340795

A geometric characterization of the groups M₁₂, He and Ru

Richard WEISS

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 4 Pages 795-814

DOI https://doi.org/10.2969/jmsj/04340795

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Published: 1991 Received: July 25, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) F. Buekenhout, Diagrams for geometries and groups, J. Combin. Theory Ser. A, 27 (1979), 121-151.
2) F. Buekenhout and X. Hubaut, Locally polar spaces and related rank 3 groups, J. Algebra, 45 (1977), 391-434.
3) R. W. Carter, Simple Groups of Lie Type, John Wiley & Sons, London, New York, 1972.
4) J. H. Conway et al., Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
5) A. Del Fra, D. Ghinelli, T. Meixner and A. Pasini, Flag-transitive extensions of C_n-geometries, Geom. Dedicata, to appear.
6) T. Meixner, Some polar towers, preprint.
7) T. Meixner, Two geometries related to the groups C0₃ and C0₁, preprint.
8) M. Ronan, Coverings of certain finite geometries, Finite Geometries and Designs, (eds P. Cameron, J. Hirschfeld and D. Hughes), London Math. Soc. Lecture Notes, 49 (1981), 316-331.
9) A. Rudvalis, A rank 3 simple group of order 2¹⁴•3³•5³•7•13•29 I, J. Algebra, 86 (1984), 181-218.
10) G. Seitz, Flag-transitive subgroups of Chevalley groups, Ann. Math., 97 (1974), 27-56.
11) M. Suzuki, A finite simple group of order 448, 345, 497, 600, Theory of Finite Groups, (eds. R. Brauer and C. Sah), Benjamin, New York, Amsterdam, 1969, pp. 113-119.
12) M. Suzuki, Transitive extensions of a class of doubly transitive groups, Nagoya Math. J., 27 (1966), 159-169.
13) J. Tits, Algebraic and abstract simple groups, Ann. Math., 80 (1964), 313-329.
14) R. Weiss and S. Yoshiara, A geometric characterization of the groups Suz and HS, J. Algebra, 133 (1990), 251-282.
15) R. Weiss, Extended generalized hexagons, Math. Proc. Cambridge Philos. Soc., 108 (1990), 7-19.
16) R. Weiss, A geometric characterization of the groups McL and C0₃, J. London Math. Soc., to appear.
17) S. Yoshiara, A classification of flag-transitive classical c. C₂-geometries by means of generators and relations, preprint.

Right : [1] F. Buekenhout, Diagrams for geometries and groups, J. Combin. Theory Ser. A, 27 (1979), 121-151.
[2] F. Buekenhout and X. Hubaut, Locally polar spaces and related rank 3 groups, J. Algebra, 45 (1977), 391-434.
[3] R. W. Carter, Simple Groups of Lie Type, John Wiley & Sons, London, New York, 1972.
[4] J. H. Conway et al., Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
[5] A. Del Fra, D. Ghinelli, T. Meixner and A. Pasini, Flag-transitive extensions of C_n-geometries, Geom. Dedicata, to appear.
[6] T. Meixner, Some polar towers, preprint.
[7] T. Meixner, Two geometries related to the groups C_0₃ and C_0₁, preprint.
[8] M. Ronan, Coverings of certain finite geometries, Finite Geometries and Designs, (eds P. Cameron, J. Hirschfeld and D. Hughes), London Math. Soc. Lecture Notes, 49 (1981), 316-331.
[9] A. Rudvalis, A rank 3 simple group of order 2¹⁴·3³·5³·7·13·29 I, J. Algebra, 86 (1984), 181-218.
[10] G. Seitz, Flag-transitive subgroups of Chevalley groups, Ann. Math., 97 (1974), 27-56.
[11] M. Suzuki, A finite simple group of order 448, 345, 497, 600, Theory of Finite Groups, (eds. R. Brauer and C. Sah), Benjamin, New York, Amsterdam, 1969, pp. 113-119.
[12] M. Suzuki, Transitive extensions of a class of doubly transitive groups, Nagoya Math. J., 27 (1966), 159-169.
[13] J. Tits, Algebraic and abstract simple groups, Ann. Math., 80 (1964), 313-329.
[14] R. Weiss and S. Yoshiara, A geometric characterization of the groups Suz and HS, J. Algebra, 133 (1990), 251-282.
[15] R. Weiss, Extended generalized hexagons, Math. Proc. Cambridge Philos. Soc., 108 (1990), 7-19.
[16] R. Weiss, A geometric characterization of the groups McL and C_0₃, J. London Math. Soc., to appear.
[17] S. Yoshiara, A classification of flag-transitive classical c. C₂-geometries by means of generators and relations, preprint.

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