Flag-transitive extensions of dual affine planes (Q1815403)

This paper classifies all finite flag-transitive geometries belonging to the string diagram obtained by juxtaposition of an \(A_n\)-diagram, a \(c\)-stroke and a dual affine plane stroke \((Af^*)\). Of course, the \(A_n\)-residue is a thin projective space, and so every stroke of the diagram could as well be labelled \(c\); hence the name \(c^n\cdot Af^*\) geometry. Also all examples of such geometries are presented. The proof of the classification is very geometric and combinatorial. Only and essentially at the beginning, group-theoretical arguments are needed. In particular the author uses the classification of finite simple groups. But this does not spoil the many beautiful geometric proofs that follow.