Proceedings of the Conference on Finite Groups
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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
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
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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