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.

In four prior volumes (Surveys of Mathematical Monographs, Volumes 40.1, 40.2, 40.3, and 40.4), the authors began the proof of the classification theorem by establishing certain uniqueness and preuniqueness results. In this volume, they now begin the proof of a major theorem from the classification grid, namely Theorem $\mathcal{C}_7$.

The book is suitable for graduate students and researchers interested in group theory.

Readership

Graduate students and research mathematicians interested in group theory.

Reviews

"This series of volumes, and this one in particular, is a model for all mathematicians of the standards and clarity that should be achieved."

-- Mathematical Reviews

Table of Contents

• Theorem $C_7$: General introduction
• General group-theoretic results
• Theorem $C^*_7$: Stage 1
• Theorem $C^*_7$: Stage 2
• Theorem $C^*_7$: Stage 3a
• Properties of $K$-groups
• Background references
• Expository references
• Glossary of symbols and terms