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Softcover ISBN:  9781470475536 
Product Code:  SURV/40.10 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470475666 
Product Code:  SURV/40.10.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470475536 
eBook ISBN:  9781470475666 
Product Code:  SURV/40.10.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 40; 2023; 570 ppMSC: Primary 20
This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see Mathematical Surveys and Monographs, Volume 40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.
ReadershipGraduate students and researchers interested in the theory of finite groups.

Table of Contents

Chapters

General grouptheoretic lemmas

Theorem $\mathscr {C}_6$ and $\mathscr {C}_6^*$

Theorems $\mathscr {C}_4$ and $\mathscr {C}_4^*$: Introduction

Theorem $\mathscr {C}_4^*$: Stage A1. First steps

Theorem $\mathscr {C}_4^*$: Stage A2. Nonconstrained $p$rank 3 centralizers

Theorem $\mathscr {C}_4^*$: Stage A3. $KM$singularities

Theorem $\mathscr {C}_4^*$: Stage A4. Setups for recognizing $G$

Theorem $\mathscr {C}_4^*$: Stage A5. Recognition

Properties of $\mathscr {K}$groups


Additional Material

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This book is the tenth in a series of volumes whose aim is to provide a complete proof of the classification theorem for the finite simple groups based on a fairly short and clearly enumerated set of background results. Specifically, this book completes our identification of the simple groups of bicharacteristic type begun in the ninth volume of the series (see Mathematical Surveys and Monographs, Volume 40.9). This is a fascinating set of simple groups which have properties in common with matrix groups (or, more generally, groups of Lie type) defined both over fields of characteristic 2 and over fields of characteristic 3. This set includes 11 of the celebrated 26 sporadic simple groups along with several of their large simple subgroups. Together with SURV/40.9, this volume provides the first unified treatment of this class of simple groups.
Graduate students and researchers interested in the theory of finite groups.

Chapters

General grouptheoretic lemmas

Theorem $\mathscr {C}_6$ and $\mathscr {C}_6^*$

Theorems $\mathscr {C}_4$ and $\mathscr {C}_4^*$: Introduction

Theorem $\mathscr {C}_4^*$: Stage A1. First steps

Theorem $\mathscr {C}_4^*$: Stage A2. Nonconstrained $p$rank 3 centralizers

Theorem $\mathscr {C}_4^*$: Stage A3. $KM$singularities

Theorem $\mathscr {C}_4^*$: Stage A4. Setups for recognizing $G$

Theorem $\mathscr {C}_4^*$: Stage A5. Recognition

Properties of $\mathscr {K}$groups