Skip to main content
Log in

The Residually Weakly Primitive Geometries of M 22

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

Abstract

We announce the classification of all firm and residually connected geometries satisfying the conditions (I P)2 and (2T)1 and on which the Mathieu group M 22 acts flag-transitively and residually weakly primitively. The complete list of geometries is available as a supplement to this note [6].

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W. Bosma, J. Cannon and C. Playoust. The Magma algebra system I: the user language, J. Symbolic Comput., No. 3/4 (1997) pp. 235–265.

    Google Scholar 

  2. F. Buekenhout, P. Cara, M. Dehon and D. Leemans, Residually weakly primitive geometries of small almost simple groups: a synthesis, preprint.

  3. M. Dehon and D. Leemans, Constructing coset geometries with Magma: an application to the sporadic groups M12 and J1, Atti Sem. Mat. Fis. Univ. Modena, (2002) pp. 415–427.

  4. M. Dehon, D. Leemans and X. Miller, The residually weakly primitive and (IP)2 geometries of M11, preprint.

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

  6. D. Leemans, Supplement to: The residually weakly primitive geometries of M 22. http://cso.ulb.ac.be/~dleemans/abstracts/m22.html (2001).

  7. D. Leemans, The residually weakly primitive geometries of J2, Note Mat., Vol. 21, No. 1 (2002) pp. 77–81.

    Google Scholar 

  8. C. Lefèvre-Percsy, N. Percsy and D. Leemans, New geometries for finite groups and polytopes, Bull. Belg. Math. Soc. Simon Stevin, Vol. 7, No. 4 (2000) pp. 583–610.

    Google Scholar 

  9. A. Pasini, A quarry of geometries, Rend. Sem. Matematico e Fisico di Milano, Vol. 65 (1995) pp. 179–247.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leemans, D. The Residually Weakly Primitive Geometries of M 22 . Designs, Codes and Cryptography 29, 177–178 (2003). https://doi.org/10.1023/A:1024160626710

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024160626710

Navigation