Groups and Geometries

1. Front Matter

   Pages i-xii

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2. Quasithin Groups

   • Michael G. Aschbacher, Stephen D. Smith

   Pages 1-7

3. The Non-canonical Gluings of two Affine Spaces

   • Barbara Baumeister, Gernot Stroth

   Pages 9-28

4. The Geometry Far from a Residue

   • Rieuwert J. Blok, Andries E. Brouwer

   Pages 29-38

5. On Flag-transitive Incidence Geometries of Rank 6 for the Mathieu Group M12

   • Francis Buekenhout, Michel Dehon, Dimitri Leemans

   Pages 39-54

6. On a Connection between Ovoids on the Hyperbolic Quadric Q ⁺(10, q) and the Lie Incidence Geometry E _6,1(q)

   • Bruce N. Cooperstein

   Pages 55-64

7. The Residually Weakly Primitive Geometries of the Janko Group J ₁

   • Harald Gottschalk, Dimitri Leemans

   Pages 65-79

8. The First Cohomology Group and Generation of Simple Groups

   • Robert M. Guralnick, Cornelius Hoffman

   Pages 81-89

9. A Characterization of the Hall-Janko Group J ₂ by a c.L*-Geometry

   • Cécile Huybrechts, Antonio Pasini

   Pages 91-106

10. Affine Extended Dual Polar Spaces

    • Alexander A. Ivanov

    Pages 107-121

11. Derivable Nets May be Embedded in Nonderivable Planes

    • Norman L. Johnson

    Pages 123-144

12. Regular Orbits and the k(GV)-Problem

    • Martin W. Liebeck

    Pages 145-148

13. Generating Minimally Transitive Groups

    • Andrea Lucchini

    Pages 149-153

14. Maximal Subgroups of Finite Exceptional Groups

    • Gary M. Seitz

    Pages 155-161

15. Subgroup Structure, Fractal Dimension, and Kac-Moody Algebras

    • Aner Shalev

    Pages 163-176

16. Aspects of Buildings

    • Ernest Shult

    Pages 177-188

17. Generalized Quadrangles Arising from Groups Generated by Abstract Transvection Groups

    • Anja Ingrid Steinbach

    Pages 189-199

18. Embeddings of Geometries in Finite Projective Spaces: a Survey

    • Josef A. Thas

    Pages 201-214

19. Affine Extensions of Near Hexagons Related to the Spin Module of Type B ₃

    • John van Bon, Hans Cuypers

    Pages 215-229

20. Ovoids and Spreads Arising from Involutions

    • Hendrik Van Maldeghem

    Pages 231-236

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.

• Group theory
• combinatorics
• geometry
• algebra
• cohomology
• finite group
• group theory

• Department of Mathematics, University of Siena, Siena, Italy

  Antonio Pasini

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