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Hardcover ISBN:  9780821827772 
Product Code:  SURV/40.6 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412715 
Product Code:  SURV/40.6.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821827772 
eBook ISBN:  9781470412715 
Product Code:  SURV/40.6.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; 2005; 529 ppMSC: Primary 20;
The classification of finite simple groups is a landmark result of modern mathematics. The original proof is spread over scores of articles by dozens of researchers. In this multivolume book, the authors are assembling the proof with explanations and references. It is a monumental task. The book, along with background from sections of the previous volumes, presents critical aspects of the classification.
Continuing the proof of the classification theorem which began in the previous five volumes (Surveys of Mathematical Monographs, Volumes 401s, 40.2, 40.3, 40.4, and 40.5), in this volume, the authors provide the classification of finite simple groups of special odd type (Theorems \(\mathcal{C}_2\) and \(\mathcal{C}_3\), as stated in the first volume of the series).
The book is suitable for graduate students and researchers interested in group theory.ReadershipGraduate students and research mathematicians interested in group theory.

Table of Contents

Part IV. The special odd case

1. General introduction to the special odd case

2. General lemmas

3. Theorem $\mathcal {C}^*_2$: Stage 1

4. Theorem $\mathcal {C}^*_2$: Stage 2

5. Theorem $\mathcal {C}_2$: Stage 3

6. Theorem $\mathcal {C}_2$: Stage 4

7. Theorem $\mathcal {C}_2$: Stage 5

8. Theorem $\mathcal {C}_3$: Stage 1

9. Theorem $\mathcal {C}_3$: Stages 2 and 3

10. $\mathrm {IV}_K$: Preliminary properties of $\mathcal {K}$groups


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This series of volumes ... is a model for all mathematicians of the standards and clarity that should be achieved.
Mathematical Reviews


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The classification of finite simple groups is a landmark result of modern mathematics. The original proof is spread over scores of articles by dozens of researchers. In this multivolume book, the authors are assembling the proof with explanations and references. It is a monumental task. The book, along with background from sections of the previous volumes, presents critical aspects of the classification.
Continuing the proof of the classification theorem which began in the previous five volumes (Surveys of Mathematical Monographs, Volumes 401s, 40.2, 40.3, 40.4, and 40.5), in this volume, the authors provide the classification of finite simple groups of special odd type (Theorems \(\mathcal{C}_2\) and \(\mathcal{C}_3\), as stated in the first volume of the series).
The book is suitable for graduate students and researchers interested in group theory.
Graduate students and research mathematicians interested in group theory.

Part IV. The special odd case

1. General introduction to the special odd case

2. General lemmas

3. Theorem $\mathcal {C}^*_2$: Stage 1

4. Theorem $\mathcal {C}^*_2$: Stage 2

5. Theorem $\mathcal {C}_2$: Stage 3

6. Theorem $\mathcal {C}_2$: Stage 4

7. Theorem $\mathcal {C}_2$: Stage 5

8. Theorem $\mathcal {C}_3$: Stage 1

9. Theorem $\mathcal {C}_3$: Stages 2 and 3

10. $\mathrm {IV}_K$: Preliminary properties of $\mathcal {K}$groups

This series of volumes ... is a model for all mathematicians of the standards and clarity that should be achieved.
Mathematical Reviews