Mathematics – Combinatorics
Scientific paper
2009-04-27
Mathematics
Combinatorics
26 pages, 5 figures
Scientific paper
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.
Cara Philippe
Devillers Alice
Giudici Michael
Praeger Cheryl E.
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