Basic coset geometries
In earlier work we gave a characterisation of pregeometries which are basic (that is, admit no non-degenerate quotients) relative to two different kinds of quotient operation, namely taking imprimitive quotients and normal quotients. Each basic geometry was shown to involve a faithful group action, which is primitive or quasiprimitive, respectively, on the set of elements of each type. For each ONan-Scott type of primitive group, we construct a new infinite family of geometries, which are thick and of unbounded rank, and which admit a flag-transitive automorphism group acting faithfully on the set of elements of each type as a primitive group of the given ONan-Scott type.
incidence geometries primitive permutation group