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Product Code:  SURV/40.9 
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Softcover ISBN:  9781470464370 
Product Code:  SURV/40.9 
List Price:  $97.00 
MAA Member Price:  $87.30 
AMS Member Price:  $77.60 
eBook ISBN:  9781470465612 
Product Code:  SURV/40.9.E 
List Price:  $97.00 
MAA Member Price:  $87.30 
AMS Member Price:  $77.60 
Softcover ISBN:  9781470464370 
eBook ISBN:  9781470465612 
Product Code:  SURV/40.9.B 
List Price:  $194.00 $145.50 
MAA Member Price:  $174.60 $130.95 
AMS Member Price:  $155.20 $116.40 

Book DetailsMathematical Surveys and MonographsVolume: 40; 2021; 520 ppMSC: Primary 20
This book is the ninth volume in a series whose goal is to furnish a careful and largely selfcontained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of \(p\)type for a suitable odd prime \(p\). It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.
ReadershipGraduate students and researchers interested in the theory of finite groups.

Table of Contents

Chapters

Introduction to theorem $\mathscr {C}_5$

General grouptheoretic lemmas, and recognition theorems

Theorem $\mathscr {C}_5$: Stage 1

Theorem $\mathscr {C}_5$: Stage 2

Theorem $\mathscr {C}_5$; State 3

Theorem $\mathcal {C}_5$: Stage 4

Theorem $\mathscr {C}^*_6$: Stage 1

Preliminary properties of $\mathscr {K}$groups


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This book is the ninth volume in a series whose goal is to furnish a careful and largely selfcontained proof of the classification theorem for the finite simple groups. Having completed the classification of the simple groups of odd type as well as the classification of the simple groups of generic even type (modulo uniqueness theorems to appear later), the current volume begins the classification of the finite simple groups of special even type. The principal result of this volume is a classification of the groups of bicharacteristic type, i.e., of both even type and of \(p\)type for a suitable odd prime \(p\). It is here that the largest sporadic groups emerge, namely the Monster, the Baby Monster, the largest Conway group, and the three Fischer groups, along with six finite groups of Lie type over small fields, several of which play a major role as subgroups or sections of these sporadic groups.
Graduate students and researchers interested in the theory of finite groups.

Chapters

Introduction to theorem $\mathscr {C}_5$

General grouptheoretic lemmas, and recognition theorems

Theorem $\mathscr {C}_5$: Stage 1

Theorem $\mathscr {C}_5$: Stage 2

Theorem $\mathscr {C}_5$; State 3

Theorem $\mathcal {C}_5$: Stage 4

Theorem $\mathscr {C}^*_6$: Stage 1

Preliminary properties of $\mathscr {K}$groups