We announce the classification of two related classes of flag-transitive geometries. There is an infinite family of such geometries, related to the nonsplit extensions 3 n 2 ] 2 ·Sp2n(2), and twelve sporadic examples coming from the simple groups M22, M23, M24, He, Co1, Co2, J4, BM , M and the nonsplit extensions 3 · M22, 323 · Co2, and 34371 · BM .

Regular polygonal complexes in euclidean 3-space E3 are discrete polyhedra-like structures with finite or infinite polygons as faces and with finite graphs as vertex-figures, such that their symmetry groups are transitive on the flags. The present paper and its predecessor describe a complete classification of regular polygonal complexes in E3. In Part I we established basic structural results ...

Let G be a group with socle a simple group of Lie type defined over the finite field with q elements where q is a power of the prime p. Suppose that G acts transitively upon the lines of a linear space S. We show that if p is significant then G acts flag-transitively on S and all examples are known. MSC(2000): 20B25, 05B05. 1 Background and statement of result A linear space S is an incidence s...

In this article, we study symmetric designs with λ prime admitting a flag-transitive and point-primitive automorphism groups G of almost simple type. We prove that either D is one the six well-known examples biplanes triplanes, or point- hyperplane design PG(n−1,q) = (q^{n−2}−1)/(q−1) X PSLn(q).

This note is part of a general programme to classify the automorphism groups of finite linear spaces. There have been a number of contributions to this programme, including two recent surveys [8, 3]. One of the most significant contributions was the classification of flag-transitive linear spaces [2]. Since then, the effort has been to classify the line-transitive examples. These fall naturally...

In this article, we investigate symmetric $(v,k,\lambda)$ designs $\mathcal{D}$ with $\lambda$ prime admitting flag-transitive and point-primitive automorphism groups $G$. We prove that if $G$ is an almost simple group socle a finite of Lie type, then either the point-hyperplane design projective space $\mathrm{PG}_{n-1}(q)$, or it parameters $(7,4,2)$, $(11,5,2)$, $(11,6,3)$ $(45,12,3)$.