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On the geometry of O’N

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Abstract

We classify the rank two BCDL 2003-geometries of O’Nan and show that the maximal rank of a BCDL 2003-geometry for O’Nan is 4. This bound is sharp since it is satisfied by the rank four geometry given by Buekenhout (Contemp Math 45:1–32, 1985).

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References

  1. Buekenhout F.: Diagrams for geometries and groups. J. Combin. Theory Ser. A 27, 121–151 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  2. Buekenhout F.: Diagram geometries for sporadic groups. Contemp. Math. 45, 1–32 (1985)

    MathSciNet  Google Scholar 

  3. Buekenhout, F. (ed.): Handbook of Incidence Geometry. Elsevier, Amsterdam (1995)

    MATH  Google Scholar 

  4. Buekenhout F., Cara P., Dehon M., Leemans D.: Residually weakly primitive geometries of small almost simple groups: a synthesis. Quaderni Mat. 12, 1–27 (2003)

    MathSciNet  Google Scholar 

  5. Buekenhout F., Cara P., Vanmeerbeek K.: Geometries of the group PSL(2, 11). Geom. Dedicata 83, 169–206 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Buekenhout, F., Dehon, M., Leemans, D.: An Atlas of residually weakly primitive geometries for small groups. Mém. Cl. Sci., Coll. 8, Ser. 3, Tome XIV. Acad. Roy. Belgique (1999)

  7. Buekenhout F., Leemans D.: On a geometry of Ivanov and Shpectorov for the O’Nan sporadic simple group. J. Combin. Theory Ser. A 85, 148–164 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Cara P., Leemans D.: The residually weakly primitive geometries of S 5 ×  2. Discrete Math. 255, 35–45 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A.: Atlas of Finite Groups. Oxford University Press, Oxford (1985)

    MATH  Google Scholar 

  10. Gottschalk H., Leemans D. et al.: The residually weakly primitive geometries of the Janko group J1. In: Pasini A., et al. (eds) Groups and Geometries, pp. 65–79. Birkhäuser, Basel (1998)

    Google Scholar 

  11. Ivanov A.A., Shpectorov S.V.: A geometry for the O’Nan-Sims group connected with the Petersen graph. Russian Math. Survey 41, 211–212 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  12. Leemans, D.: On computing the subgroup lattice of O′N. Preprint. See http://cso.ulb.ac.be/~dleemans/abstracts/onlat.html

  13. Leemans D.: An atlas of regular thin geometries for small groups. Math. Comput. 68, 1631–1647 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Leemans, D.: Residually weakly primitive and locally two-transitive geometries for sporadic groups. Mém. Cl. Sci., Coll. 4, Ser. 3, Tome XI. Acad. Roy. Belgique (2008)

  15. Tits, J.: Géométries polyédriques et groupes simples. Atti 2a Riunione Groupem. Math. Express. Lat. Firenze, pp. 66–88 (1963)

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  1. Département de Mathématiques, Université Libre de Bruxelles, Service de Géométrie, C.P. 216, Boulevard du Triomphe, 1050, Brussels, Belgium

    Dimitri Leemans

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  1. Dimitri Leemans
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Correspondence to Dimitri Leemans.

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This research was accomplished while the author was visiting the Magma group at the University of Sydney. We gratefully acknowledge support from the University of Sydney, the Belgian National Fund for Scientific Research, and the “Communauté Française de Belgique-Actions de Recherche Concertées”.

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Leemans, D. On the geometry of O’N. J. Geom. 97, 83–97 (2010). https://doi.org/10.1007/s00022-010-0042-2

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