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Hardcover ISBN:  9781470441890 
Product Code:  SURV/40.8 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
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Product Code:  SURV/40.8.E 
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Hardcover ISBN:  9781470441890 
eBook ISBN:  9781470450595 
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Book DetailsMathematical Surveys and MonographsVolume: 40; 2018; 488 ppMSC: Primary 20
This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series—the completion of the proof of the following theorem:
Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups.
Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.
ReadershipGraduate students and researchers interested in the theory of finite groups.

Table of Contents

Chapters

Introduction

Recognition theory

Theorem $\mathscr {C}^*_7$: Stage 4b$+$—A large Lietype subgroup $G_0$ for $p=2$

Theorem $\mathscr {C}^*_7$: Stage 4b$+$—A large Lietype subgroup $G_0$ for $p>2$

Theorem $\mathscr {C}^*_7$: Stage 5$+$: $G=G_0$

Preliminary properties of $\mathscr {K}$groups


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This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series—the completion of the proof of the following theorem:
Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups.
Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.
Graduate students and researchers interested in the theory of finite groups.

Chapters

Introduction

Recognition theory

Theorem $\mathscr {C}^*_7$: Stage 4b$+$—A large Lietype subgroup $G_0$ for $p=2$

Theorem $\mathscr {C}^*_7$: Stage 4b$+$—A large Lietype subgroup $G_0$ for $p>2$

Theorem $\mathscr {C}^*_7$: Stage 5$+$: $G=G_0$

Preliminary properties of $\mathscr {K}$groups