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Finite and Locally Finite Groups

  • Book
  • © 1995

Overview

Editors:
  1. B. Hartley

    1. Department of Mathematics, University of Manchester, Manchester, UK

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  2. G. M. Seitz

    1. Department of Mathematics, University of Oregon, Eugene, USA

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  3. A. V. Borovik

    1. UMIST, Manchester, UK

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  4. R. M. Bryant

    1. UMIST, Manchester, UK

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Part of the book series: Nato Science Series C: (ASIC, volume 471)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii
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  2. Simple Locally Finite Groups

    • B. Hartley
    Pages 1-44

  3. Algebraic Groups

    • G. M. Seitz
    Pages 45-70

  4. Subgroups of Simple Algebraic Groups and of Related Finite and Locally Finite Groups of Lie Type

    • M. W. Liebeck
    Pages 71-96

  5. Finite Simple Groups and Permutation Groups

    • J. Saxl
    Pages 97-110

  6. Finitary Linear Groups: A Survey

    • R. E. Phillips
    Pages 111-146

  7. Locally Finite Simple Groups of Finitary Linear Transformations

    • J. I. Hall
    Pages 147-188

  8. Non-Finitary Locally Finite Simple Groups

    • U. Meierfrankenfeld
    Pages 189-212

  9. Inert Subgroups in Simple Locally Finite Groups

    • V. V. Belyaev
    Pages 213-218

  10. Group Rings of Simple Locally Finite Groups

    • A. E. Zalesskiĭ
    Pages 219-246

  11. Simple Locally Finite Groups of Finite Morley Rank and Odd Type

    • A. V. Borovik
    Pages 247-284

  12. Existentially Closed Groups in Specific Classes

    • F. Leinen
    Pages 285-326

  13. Groups Acting on Polynomial Algebras

    • R. M. Bryant
    Pages 327-346

  14. Characters and Sets of Primes for Solvable Groups

    • I. M. Isaacs
    Pages 347-376

  15. Character Theory and Length Problems

    • A. Turull
    Pages 377-400

  16. Finite p-Groups

    • A. Shalev
    Pages 401-450

  17. Back Matter

    Pages 451-458
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Keywords

About this book

This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni

Editors and Affiliations

  • Department of Mathematics, University of Manchester, Manchester, UK

    B. Hartley

  • Department of Mathematics, University of Oregon, Eugene, USA

    G. M. Seitz

  • UMIST, Manchester, UK

    A. V. Borovik, R. M. Bryant

Bibliographic Information

  • Book Title: Finite and Locally Finite Groups

  • Editors: B. Hartley, G. M. Seitz, A. V. Borovik, R. M. Bryant

  • Series Title: Nato Science Series C:

  • DOI: https://doi.org/10.1007/978-94-011-0329-9

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1995

  • Hardcover ISBN: 978-0-7923-3669-3Published: 31 August 1995

  • Softcover ISBN: 978-94-010-4145-4Published: 21 October 2012

  • eBook ISBN: 978-94-011-0329-9Published: 06 December 2012

  • Series ISSN: 1389-2185

  • Edition Number: 1

  • Number of Pages: XII, 458

  • Topics: Group Theory and Generalizations, Associative Rings and Algebras

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