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The Classification of the Finite Simple Groups, Number 10: Part V, Chapters 9–17: Theorem $C_6$ and Theorem $C^*_4$, Case A
 
Inna Capdeboscq University of Warwick, Coventry, United Kingdom
Richard Lyons Rutgers University, Piscataway, NJ
Ronald Solomon The Ohio State University, Columbus, OH
Softcover ISBN:  978-1-4704-7553-6
Product Code:  SURV/40.10
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-7566-6
Product Code:  SURV/40.10.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7553-6
eBook: ISBN:  978-1-4704-7566-6
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
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The Classification of the Finite Simple Groups, Number 10: Part V, Chapters 9–17: Theorem $C_6$ and Theorem $C^*_4$, Case A
Inna Capdeboscq University of Warwick, Coventry, United Kingdom
Richard Lyons Rutgers University, Piscataway, NJ
Ronald Solomon The Ohio State University, Columbus, OH
Softcover ISBN:  978-1-4704-7553-6
Product Code:  SURV/40.10
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-7566-6
Product Code:  SURV/40.10.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-1-4704-7553-6
eBook ISBN:  978-1-4704-7566-6
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 Details
     
     
    Mathematical Surveys and Monographs
    Volume: 402023; 570 pp
    MSC: 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.

    Readership

    Graduate students and researchers interested in the theory of finite groups.

  • Table of Contents
     
     
    • Chapters
    • General group-theoretic 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
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 402023; 570 pp
MSC: 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.

Readership

Graduate students and researchers interested in the theory of finite groups.

  • Chapters
  • General group-theoretic 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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