Quotients of incidence geometries
Copyright policy )Quotients of incidence geometries
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.
26 pages, 5 figures
- Vrije Universiteit Brussel Belgium
- University of Western Australia Australia
05B25, 51E24, 20B25, Finite automorphism groups of algebraic, geometric, or combinatorial structures, incidence geometry, Group Theory (math.GR), pregeometry, coset geometry, normal quotient, Buildings and the geometry of diagrams, flag transitive geometry, FOS: Mathematics, quotient, Mathematics - Combinatorics, flag-transitive geometry, Combinatorial aspects of finite geometries, Combinatorics (math.CO), Mathematics - Group Theory
05B25, 51E24, 20B25, Finite automorphism groups of algebraic, geometric, or combinatorial structures, incidence geometry, Group Theory (math.GR), pregeometry, coset geometry, normal quotient, Buildings and the geometry of diagrams, flag transitive geometry, FOS: Mathematics, quotient, Mathematics - Combinatorics, flag-transitive geometry, Combinatorial aspects of finite geometries, Combinatorics (math.CO), Mathematics - Group Theory
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