Quotients of incidence geometries

Authors:
Philippe Cara;Alice Devillers;Michael Giudici;Cheryl E. Praeger
Affiliations:
Department of Mathematics, Vrije Universiteit Brussel, Brussel, Belgium 1050;Centre for Mathematics of Symmetry and Computation/School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia 6009;Centre for Mathematics of Symmetry and Computation/School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia 6009;Centre for Mathematics of Symmetry and Computation/School of Mathematics and Statistics, The University of Western Australia, Crawley, Australia 6009
Venue:
Designs, Codes and Cryptography
Year:
2012

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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.