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The Classification of the Finite Simple Groups, Number 9: Part V, Chapters 1-8: Theorem $C_5$ and Theorem $C_6$, Stage 1
 
Inna Capdeboscq University of Warwick, Coventry, United Kingdom
Richard Lyons Rutgers University, Piscataway, NJ
Ronald Solomon The Ohio State University, Columbus, OH
The Classification of the Finite Simple Groups, Number 9
Softcover ISBN:  978-1-4704-6437-0
Product Code:  SURV/40.9
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
eBook ISBN:  978-1-4704-6561-2
Product Code:  SURV/40.9.E
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
Softcover ISBN:  978-1-4704-6437-0
eBook: ISBN:  978-1-4704-6561-2
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
The Classification of the Finite Simple Groups, Number 9
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The Classification of the Finite Simple Groups, Number 9: Part V, Chapters 1-8: Theorem $C_5$ and Theorem $C_6$, Stage 1
Inna Capdeboscq University of Warwick, Coventry, United Kingdom
Richard Lyons Rutgers University, Piscataway, NJ
Ronald Solomon The Ohio State University, Columbus, OH
Softcover ISBN:  978-1-4704-6437-0
Product Code:  SURV/40.9
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
eBook ISBN:  978-1-4704-6561-2
Product Code:  SURV/40.9.E
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
Softcover ISBN:  978-1-4704-6437-0
eBook ISBN:  978-1-4704-6561-2
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 Details
     
     
    Mathematical Surveys and Monographs
    Volume: 402021; 520 pp
    MSC: Primary 20;

    This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained 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.

    Readership

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

  • Table of Contents
     
     
    • Chapters
    • Introduction to theorem $\mathscr {C}_5$
    • General group-theoretic 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
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 402021; 520 pp
MSC: Primary 20;

This book is the ninth volume in a series whose goal is to furnish a careful and largely self-contained 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.

Readership

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

  • Chapters
  • Introduction to theorem $\mathscr {C}_5$
  • General group-theoretic 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.