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Geometries and Groups

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

  • Conference proceedings
  • © 1988

Overview

Editors:
  1. M. Aschbacher

    1. CalTech, Pasadena, USA

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  2. A. M. Cohen

    1. CWI, Amsterdam, The Netherlands

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  3. W. M. Kantor

    1. IAS, Princeton, USA

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Table of contents (21 papers)

  1. Front Matter

    Pages i-2
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  2. Diagram Geometries and Chamber Systems with Transitive Groups

    1. Front Matter

      Pages 3-3
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    2. On Amalgamation of Rank 1 parabolic Groups

      • F. G. Timmesfeld
      Pages 5-70

    3. One Node Extensions of Buildings

      • G. Stroth
      Pages 71-120

    4. Reflections on Concrete Buildings

      • William M. Kantor
      Pages 121-145

    5. Folding Down Classical Tits Chamber Systems

      • Thomas Meixner
      Pages 147-157

    6. On the uniqueness of the Co1 2-local geometry

      • Yoav Segev
      Pages 159-219

  3. Incidence Systems

    1. Front Matter

      Pages 221-221
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    2. Remarks on Geometries of Type CN

      • Ernest Shult
      Pages 223-268

    3. On the Foundations of Incidence Geometry

      • Francis Buekenhout, Dominique Buset
      Pages 269-296

    4. A Characterization of Point-Line Geometries for Finite Buildings

      • G. Hanssens
      Pages 297-315

    5. Geometries of Type Cn and F4 with Flag-Transitive Automorphism Groups

      • Antonio Pasini
      Pages 317-337

    6. Geometric Sets of Permutations

      • P. J. Cameron
      Pages 339-351

  4. Chevalley Groups

    1. Front Matter

      Pages 353-353
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    2. Geometric Techniques in Representation Theory

      • Stephen D. Smith
      Pages 355-373

    3. A Survey of the Maximal Subgroups of the Finite Simple Groups

      • Peter B. Kleidman, Martin W. Liebeck
      Pages 375-389

    4. Representations and Maximal Subgroups of Finite Groups of Lie Type

      • Gary M. Seitz
      Pages 391-406

    5. Some representations of exceptional Lie algebras

      • Peter B. Gilkey, Gary M. Seitz
      Pages 407-416

    6. Some Multilinear Forms with Large Isometry Groups

      • Michael Aschbacher
      Pages 417-465

    7. The 2-spaces of the standard E 6(q)-module

      • Arjeh M. Cohen, Bruce N. Cooperstein
      Pages 467-480
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Keywords

About this book

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.

Editors and Affiliations

  • CalTech, Pasadena, USA

    M. Aschbacher

  • CWI, Amsterdam, The Netherlands

    A. M. Cohen

  • IAS, Princeton, USA

    W. M. Kantor

Bibliographic Information

  • Book Title: Geometries and Groups

  • Book Subtitle: Proceedings of the Workshop Geometries and Groups, Finite and Algebraic, Noorwijkerhout, Holland, March 1986

  • Editors: M. Aschbacher, A. M. Cohen, W. M. Kantor

  • DOI: https://doi.org/10.1007/978-94-009-4017-8

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1988

  • Hardcover ISBN: 978-90-277-2623-0Published: 31 January 1988

  • Softcover ISBN: 978-94-010-8282-2Published: 05 November 2011

  • eBook ISBN: 978-94-009-4017-8Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 542

  • Topics: Geometry

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