The Classification of the Finite Simple Groups, Number 8: Part III, Chapters 12-17: the Generic Case, Completed (Mathematical Surveys and Monographs) - Hardcover

Daniel Gorenstein (author), Richard Lyons (author) & Ronald Solomon (author)

Hardcover

ISBN 10: 1470441896 ISBN 13: 9781470441890

Publisher: American Mathematical Society, 2019

Synopsis

This book completes a trilogy (Numbers 5, 7, and 8) of the series The Classification of the Finite Simple Groups treating the generic case of the classification of the finite simple groups. In conjunction with Numbers 4 and 6, it allows us to reach a major milestone in our series--the completion of the proof of the following theorem: Theorem O: Let G be a finite simple group of odd type, all of whose proper simple sections are known simple groups. Then either G is an alternating group or G is a finite group of Lie type defined over a field of odd order or G is one of six sporadic simple groups.

Put another way, Theorem O asserts that any minimal counterexample to the classification of the finite simple groups must be of even type. The work of Aschbacher and Smith shows that a minimal counterexample is not of quasithin even type, while this volume shows that a minimal counterexample cannot be of generic even type, modulo the treatment of certain intermediate configurations of even type which will be ruled out in the next volume of our series.

About this title

About the Author

Daniel Gorenstein and Richard Lyons, Rutgers University, Piscataway, NJ.

Ronald Solomon, The Ohio State University, Columbus, OH.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 1470441896
• ISBN 13: 9781470441890
• Binding: Hardcover
• Number of pages: 488