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Designs, Codes and Cryptography

, Volume 64, Issue 1–2, pp 105–128 | Cite as

Quotients of incidence geometries

  • Philippe Cara
  • Alice Devillers
  • Michael Giudici
  • Cheryl E. Praeger
Article

Abstract

We develop a theory for quotients of geometries and obtain sufficient conditions for the quotient of a geometry to be a geometry. These conditions are compared with earlier work on quotients, in particular by Pasini and Tits. We also explore geometric properties such as connectivity, firmness and transitivity conditions to determine when they are preserved under the quotienting operation. We show that the class of coset pregeometries, which contains all flag-transitive geometries, is closed under an appropriate quotienting operation.

Keywords

Incidence geometry Coset geometry Quotient Normal quotient Pregeometry Flag transitive geometry 

Mathematics Subject Classification (2000)

05B25 51E24 20B25 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Philippe Cara
    • 1
  • Alice Devillers
    • 2
  • Michael Giudici
    • 2
  • Cheryl E. Praeger
    • 2
  1. 1.Department of MathematicsVrije Universiteit BrusselBrusselBelgium
  2. 2.Centre for Mathematics of Symmetry and Computation/School of Mathematics and StatisticsThe University of Western AustraliaCrawleyAustralia

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