Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T13:16:13.696Z Has data issue: false hasContentIssue false
  • English
  • Français

Extended generalized hexagons

Published online by Cambridge University Press:  24 October 2008

Richard Weiss
Richard Weiss
Affiliation:
Department of Mathematics, Tufts University, Medford, MA 02155, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

As in [2], we define a geometry Γ = (B2, …, Br; *) to be an ordered sequence of r pairwise disjoint non-empty sets Bi together with a symmetric incidence relation * on their union B = B1 ∪ … ∪ Br such that if F is any maximal set of pairwise incident elements (i.e. a maximal flag), then |F ∩ Bi| = 1 for i = 1,…, r. The number r is called the rank of Γ. The geometry Γ is called connected if the r-partite graph (Γ, *) is connected.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 1 , July 1990 , pp. 7 - 19
Copyright
Copyright © Cambridge Philosophical Society 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Buekenhout, F. and Hubaut, X.. Locally polar spaces and related rank 3 groups. J. Algebra 45 (1977), 391–434.CrossRefGoogle Scholar
[2]Buekenhout, F.. Diagrams for geometries and groups. J. Combin. Theory Ser. A 27 (1979), 121–151.CrossRefGoogle Scholar
[3]Carter, R. W.. Simple Groups of Lie Type (John Wiley & Sons, 1972).Google Scholar
[4]Ronan, M.. Coverings of certain finite geometries. In Finite Geometries and Designs, London Math. Soc. Lecture Note Ser. no. 49 (Cambridge University Press, 1981), pp. 316–331.CrossRefGoogle Scholar
[5]Seitz, G.. Flag-transitive subgroups of Chevalley groups. Ann. of Math. (2) 97 (1974), 27–56.CrossRefGoogle Scholar
[6]Suzuki, M.. A finite simple group of order 448, 345, 497, 600. In Theory of Finite Groups (eds. Brauer, R. and Sah, C.) (Benjamin, 1969), pp. 113–119.Google Scholar
[7]Suzuki, M.. Transitive extensions of a class of doubly transitive groups. Nagoya Math. J. 27 (1966), 159–169.CrossRefGoogle Scholar
[8]Weiss, R. and Yoshiara, S.. A geometric characterization of the groups Suz and HS. J. Algebra (to appear).Google Scholar