Geometries and Groups Proceedings of the Workshop Geometries and Groups, Finite and Algebraic, Noorwijkerhout, Holland, March 1986

The workshop was set up in order to stimulate the interaction between (finite and algebraic) geometries and groups. Five areas of concentrated research were chosen on which attention would be focused, namely: diagram geometries and chamber systems with transitive automorphism groups, geometries viewed as incidence systems, properties of finite groups of Lie type, geometries related to finite simple groups, and algebraic groups. The list of talks (cf. page iii) illustrates how these subjects were represented during the workshop. The contributions to these proceedings mainly belong to the first three areas; therefore, (i) diagram geometries and chamber systems with transitive automorphism groups, (ii) geometries viewed as incidence systems, and (iii) properties of finite groups of Lie type occur as section titles. The fourth and final section of these proceedings has been named graphs and groups; besides some graph theory, this encapsules most of the work related to finite simple groups that does not (explicitly) deal with diagram geometry. A few more words about the content: (i). Diagram geometries and chamber systems with transitive automorphism groups. As a consequence of Tits' seminal work on the subject, all finite buildings are known. But usually, in a situation where groups are to be characterized by certain data concerning subgroups, a lot less is known than the full parabolic picture corresponding to the building.

Content.- (i) Diagram Geometries and Chamber Systems with Transitive Groups.- On Amalgamation of Rank 1 Parabolic Groups.- One Node Extensions of Buildings.- Reflections on Concrete Buildings.- Folding Down Classical Tits Chamber Systems.- On the Uniqueness of the Co1 2-Local Geometry.- (ii) Incidence Systems.- Remarks on Geometries of Type CN.- On the Foundations of Incidence Geometry.- A Characterization of Point-Line Geometries for Finite Buildings.- Geometries of Type Cn and F4 with Flag-Transitive Groups.- Geometric Sets of Permutations.- (iii) Chevalley Groups.- Geometric Techniques in Representation Theory.- A Survey of the Maximal Subgroups of the Finite Simple Groups.- Representations and Maximal Subgroups of Finite Groups of Lie Type.- Some Representations of Exceptional Lie Algebras.- Some Multilinear Forms with Large Isometry Groups.- The 2-Spaces of the E6(q)-Module.- (iv) Graphs and Groups.- On the Group Fi24.- A First Step Toward the Classification of Fischer Groups.- Modified Steinberg Relations for the Group J4.- Geodetic Graphs of Diameter Two.- Symmetrical Maps Arising from Regular Coxeter Elements of Linear Groups.