On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. It brought together experts and interested mathematicians from numerous countries. The scientific program centered around invited exposi tory lectures; there also were shorter research announcements, including talks by younger researchers. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. Special attention was drawn to the interplay between group-theoretic methods and geometric and combinatorial ones. Expanded versions of many of the talks appear in these Proceedings. This volume is intended to provide a stimulating collection of themes for a broad range of algebraists and geometers. Among those themes, represented within the conference or these Proceedings, are aspects of the following: 1. the classification of finite simple groups, 2. the structure and properties of groups of Lie type over finite and algebraically closed fields of finite characteristic, 3. buildings, and the geometry of projective and polar spaces, and 4. geometries of sporadic simple groups. We are grateful to the authors for their efforts in providing us with manuscripts in LaTeX. Barbara Priwitzer and Thomas Hintermann, Mathematics Editors of Birkhauser, have been very helpful and supportive throughout the preparation of this volume.
Table of ContentsQuasithin groups.- The non-canonical gluings of two affine spaces.- The geometry far from a residue.- On flag-transitive incidence geometries of rank 6 for the Mathieu group M12.- On a connection between ovoids on the hyperbolic quadric Q+(10, q) and the Lie incidence geometry E6,1 (q).- The residually weakly primitive geometries of the Janko group J1.- The first cohomology group and generation of simple groups.- A characterization of the Hall-Janko group J2 by a c.L* -geometry.- Affine extended dual polar spaces.- Derivable nets may be embedded in nonderivable planes.- Regular orbits and the k(GV)-problem.- Generating minimally transitive groups.- Maximal subgroups of finite exceptional groups.- Subgroup structure, fractal dimension, and Kac-Moody algebras.- Aspects of buildings.- Generalized quadrangles arising from groups generated by abstract transvection groups.- Embeddings of geometries in finite protective spaces: a survey.- Affine extensions of near hexagons related to the spin module of type B3.- Ovoids and spreads arising from involutions.- The Borel-Tits property for finite groups.- Generalized reflection groups I. Constructing the algebra.