Character Theory for the Odd Order Theorem

T. Peterfalvi; R. Sandling

doi:10.1017/CBO9780511565861

The famous and important theorem of W. Feit and J. G. Thompson states that every group of odd order is solvable, and the proof of this has roughly two parts. The first part appeared in Bender and Glauberman's Local Analysis for the Odd Order Theorem which was number 188 in this series. This book, first published in 2000, provides the character-theoretic second part and thus completes the proof. Also included here is a revision of a theorem of Suzuki on split BN-pairs of rank one; a prerequisite for the classification of finite simple groups. All researchers in group theory should have a copy of this book in their library.

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Character Theory for the Odd Order Theorem

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Contents

Frontmatter
pp i-iv

Cotents
pp v-vi

Preface
pp vii-viii

Part I - Character Theory for the Odd Order Theorem

Introduction
pp 1-2

Notation
pp 3-4

1 - Preliminary Results from Character Theory
pp 5-9

2 - The Dade Isometry
pp 10-14

3 - TI-Subsets with Cyclic Normalizers
pp 15-20

4 - The Dade Isometry for a Certain Type of Subgroup
pp 21-24

5 - Coherence
pp 25-29

6 - Some Coherence Theorems
pp 30-37

7 - Non-existence of a Certain Type of Group of Odd Order
pp 38-43

8 - Structure of a Minimal Simple Group of Odd Order
pp 44-49

9 - On the Maximal Subgroups of G of Types II, III and IV
pp 50-57

10 - Maximal Subgroups of Types III, IV and V
pp 58-63

11 - Maximal Subgroups of Types III and IV
pp 64-68

12 - Maximal Subgroups of Type I
pp 69-74

13 - The Subgroups S and T
pp 75-86

14 - Non-existence of G
pp 87-92

Notes
pp 93-94

References
pp 95-96

Part II - A Theorem of Suzuki

Introduction
pp 97-98

Notation
pp 99-99

Chapter I - General Properties of G
pp 100-107

Chapter II - The First Case
pp 108-114

Chapter III - The Structure of H
pp 115-121

Chapter IV - Characterization of PSU(3, q)
pp 122-134

Appendix I - A Special Case of a Theorem of Huppert
pp 135-136

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Character Theory for the Odd Order Theorem

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