Proceedings of the Conference on Finite Groups

Proceedings of the Conference on Finite Groups

1st Edition - January 1, 1976

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  • Editors: William R. Scott, Fletcher Gross
  • eBook ISBN: 9781483261089

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Proceedings of the Conference on Finite Groups provides information pertinent to the fundamental aspects of finite group theory. This book presents the problem of characterizing simple groups in terms of the local structure of a group. Organized into five parts encompassing 43 chapters, this book begins with an overview of the characterization of the Chevalley groups over fields of odd order and indicates the role of this characterization in the theory of component type groups. This text then examines the structure as well as the representations of specific simple groups. Other chapters consider the general theory of representations and characters of finite groups. This book discusses as well permutation groups and the connection between group theory and geometry. The final chapter deals with finite solvable groups as well as the theory of formations. This book is a valuable resource for mathematicians, graduate students, and research workers.

Table of Contents

  • List of Contributors


    Part I. Local Structure

    A Characterization of Certain Chevalley Groups and Its Application to Component Type Groups

    Finite Groups of Alternating Type

    Finite Groups of 2-Local 3-Rank at Most 1

    Finite Simple Groups of Characteristic 2,3-Type

    3-Structure in Finite Simple Groups

    Finite Groups of PSL(2,q)-Type

    Some Characterizations by Centralizers of Elements of Order Three

    A Characterization of PSp4(3m) by the Gentralizer of an Element of Order Three

    Characterization of 3D4(q3),q = 2n by Its Sylow 2-Subgroup

    Signalizer Functors

    Strongly Closed 2-Subgroups of Finite Groups

    Part II. The Known Simple Groups

    The Structure of the "Monster" Simple Groups

    On the Simple Group F of Order 214 · 36 · 56 · 7 · 11 · 19

    A Monomial Character of Fischer's Baby Monster

    On the Irreducible Characters of a Simple Group of Order 241 · 313 · 56 · 72 · 11 · 13 · 17 · 19 · 23 · 31 · 47

    A Setting for the Leech Lattice

    The Submodule Construction of Weyl Modules for Groups of Type A1

    On the 1-Cohomology of Finite Groups of Lie Type

    Field Automorphisms and Maximal Subgroups of Finite Chevalley Groups

    On the Degrees of Certain Characters of Chevalley Groups

    Part III. Representations

    The Main Problem of Block Theory

    On Projective Representations of Finite Wreath Products

    Theorems Relating Finite Groups and Division Algebras

    Exceptional Characters of Finite Groups with a Frobenius Subgroup

    Simple Groups with a Cyclic Sylow Subgroup

    On Finite Linear Groups in Dimension at Most 10

    Nonexistence of a Finite Group with a Specified 7-Block

    Linear Groups Containing an Element with an Eigenspace of Codimension Two

    On Finite Complex Linear Groups of Degree (q-l)/2

    Sylow Automizers of Odd Order or An Application of Coherence

    On Groups of Central Type

    Part IV. Permutation Groups

    Two-Transitive Extensions of Some Groups

    The Non-Existence of Rank-3 Transitive Extensions of the Higman-Sims Simple Group

    On the n,2n Problem of Michael Fried

    Block Designs from Frobenius Groups and Planar Near-Rings

    Geometry of Groups of Lie Type

    Locally Dual Affine Geometries

    Part V. Solvable Groups

    The Hughes Problem and Generalizations

    A Normalizer Condition on Finite p-Groups

    Products of Formations

    p-n Groups and p-Saturated Formations

    Irreducible Modules of Solvable Groups Are Algebraic

    Certain Frobenius Groups Acting Fixed-Point-Free on Solvable Groups

    Bounding the Fitting Length of a Finite Group

Product details

  • No. of pages: 580
  • Language: English
  • Copyright: © Academic Press 1976
  • Published: January 1, 1976
  • Imprint: Academic Press
  • eBook ISBN: 9781483261089

About the Editors

William R. Scott

Fletcher Gross

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