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.

Publication year:2012

Keywords:incidence geometry, coset geometry, quotient, normal quotient, pregeometry, flag-transitive geometry