Quotients of incidence geometries |
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| Authors: | Philippe Cara Alice Devillers Michael Giudici Cheryl E Praeger |
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| Institution: | 1. Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussel, Belgium
2. Centre for Mathematics of Symmetry and Computation/School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia
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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. |
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