Proceedings of the Conference on Finite Groups

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.

List of Contributors

Preface

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