Skip to main content
SpringerLink
Log in

A rank six geometry related to the McLaughlin sporadic simple group

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

In the literature, there are but a few incidence geometries on which the McLaughlin sporadic group \({\mathsf{McL}}\) acts as a flag-transitive automorphism group. Their highest rank is four. In the present paper, we construct a geometry of rank six on which \({\mathsf{McL}}\) acts flag-transitively and which has the following diagram.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

  3. Buekenhout F (ed) (1995). Handbook of incidence geometry. Buildings and foundations. Elsevier, Amsterdam

    MATH  Google Scholar 

  4. Diawara O (1984) Sur le groupe simple de J. McLaughlin PhD thesis, Université Libre de Bruxelles

  5. Gottschalk H and Leemans D (2003). Geometries for the group PSL(3,4). Eur J Combin 24: 267–291

    Article  MATH  Google Scholar 

  6. Hartley MI (2005) Polytopes derived from sporadic simple groups – auxiliary information. http://www.dr-mikes-maths.com/sporpolys/

  7. Ivanov AA (1999) Geometry of sporadic groups I. Petersen and tilde geometries. Number 76 in encyclopedia of mathematics and its applications. Cambridge University Press

  8. Ivanov AA and Shpectorov SV (1988). Geometries for sporadic groups related to the Petersen graph. I. Commun Algebra 16(5): 925–953

    Article  MATH  Google Scholar 

  9. McLaughlin J (1969) A simple group of order 898,128,000. In: Theory of Finite Groups. Symposium, Harvard Univ., Cambridge, Mass., 1968, Benjamin, New York, pp 109–111

  10. Pasini A (1994) Diagram geometries. Oxford University Press

  11. Ronan M and Stroth G (1984). Minimal parabolic geometries for the sporadic groups. Eur J Comb 5: 59–91

    MATH  Google Scholar 

  12. Stroth G (1989). Some geometry for McL. Commun Algebra 17(11): 2825–2833

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématique, C.P.216-Géométrie, Combinatoire et Théorie des groupes, Université Libre de Bruxelles, Boulevard du Triomphe, Bruxelles, 1050, Belgium

    Francis Buekenhout & Dimitri Leemans

Authors
  1. Francis Buekenhout
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dimitri Leemans
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dimitri Leemans.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buekenhout, F., Leemans, D. A rank six geometry related to the McLaughlin sporadic simple group. Des. Codes Cryptogr. 44, 151–155 (2007). https://doi.org/10.1007/s10623-007-9082-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-007-9082-5

Keywords

AMS Classification

Search

Navigation