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Symplectic Amalgams

  • Book
  • © 2002

Overview

Authors:
  1. Christopher Parker

    1. School of Mathematics and Statistics, University of Birmingham, Birmingham, UK

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  2. Peter Rowley

    1. Department of Mathematics, University of Manchester Institute of Science and Technology, Manchester, UK

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  • Written by two of the world's most notable specialists in group amalgams Collates in one volume results that have previously been published in various research papers Provides a complete survey of the field, accessible to both specialists and non-specialists alike

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Christopher Parker, Peter Rowley
    Pages 1-19

  3. Preliminaries

    • Christopher Parker, Peter Rowley
    Pages 21-51

  4. The Structure of SL2(q) and its Modules

    • Christopher Parker, Peter Rowley
    Pages 53-66

  5. Elementary Properties of Symplectic Amalgams

    • Christopher Parker, Peter Rowley
    Pages 67-80

  6. The Structure of Qα

    • Christopher Parker, Peter Rowley
    Pages 81-92

  7. The L β-Chief Factors in V β

    • Christopher Parker, Peter Rowley
    Pages 93-112

  8. Reduced Symplectic Amalgams

    • Christopher Parker, Peter Rowley
    Pages 113-123

  9. The Largest Normal p′-Subgroup of L β/Q β

    • Christopher Parker, Peter Rowley
    Pages 125-140

  10. The Components of Lβ/Qβ

    • Christopher Parker, Peter Rowley
    Pages 141-162

  11. The Reduction to Quasisimple when \( C_{U_\alpha } (U_\alpha /Z_\alpha ) \nleqslant Q_\beta \)

    • Christopher Parker, Peter Rowley
    Pages 163-176

  12. A First Look at the Amalgams with |V β/Z(V β)| = q 4

    • Christopher Parker, Peter Rowley
    Pages 177-186

  13. The Story so Far

    • Christopher Parker, Peter Rowley
    Pages 187-188

  14. Groups of Lie Type

    • Christopher Parker, Peter Rowley
    Pages 189-213

  15. Modules for Groups of Lie Type

    • Christopher Parker, Peter Rowley
    Pages 215-247

  16. Sporadic Simple Groups and Their Modules

    • Christopher Parker, Peter Rowley
    Pages 249-255

  17. Alternating Groups and Their Modules

    • Christopher Parker, Peter Rowley
    Pages 257-264

  18. Rank One Groups

    • Christopher Parker, Peter Rowley
    Pages 265-270

  19. Lie Type Groups in Characteristic p and Rank ≥ 2

    • Christopher Parker, Peter Rowley
    Pages 271-291

  20. Lie Type Groups and Natural Modules

    • Christopher Parker, Peter Rowley
    Pages 293-311
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Keywords

About this book

The aim of this book is the classification of symplectic amalgams - structures which are intimately related to the finite simple groups. In all there sixteen infinite families of symplectic amalgams together with 62 more exotic examples. The classification touches on many important aspects of modern group theory: * p-local analysis * the amalgam method * representation theory over finite fields; and * properties of the finite simple groups. The account is for the most part self-contained and the wealth of detail makes this book an excellent introduction to these recent developments for graduate students, as well as a valuable resource and reference for specialists in the area.

Authors and Affiliations

  • School of Mathematics and Statistics, University of Birmingham, Birmingham, UK

    Christopher Parker

  • Department of Mathematics, University of Manchester Institute of Science and Technology, Manchester, UK

    Peter Rowley

Bibliographic Information

  • Book Title: Symplectic Amalgams

  • Authors: Christopher Parker, Peter Rowley

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4471-0165-9

  • Publisher: Springer London

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag London 2002

  • Hardcover ISBN: 978-1-85233-430-7Published: 26 April 2002

  • Softcover ISBN: 978-1-4471-1088-0Published: 08 October 2012

  • eBook ISBN: 978-1-4471-0165-9Published: 06 December 2012

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XI, 361

  • Topics: Geometry, Group Theory and Generalizations

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