The geometry of Dowling lattices (Q1328497)

Dowling lattices are a class of lattices which are defined in terms of groups and partitions of finite sets. The goal of the paper is to employ techniques inspired by classical geometry to reconstruct the group from a Dowling lattice. The techniques are similar to those used in the foundations of geometry to coordinatize an affine or projective space by constructing a corresponding field. Also discussed are the implications of imposing Desargues' Theorem and Pappus' Theorem on certain structures derived from an axiomatic approach to Dowling lattices.