The Classification of the Finite Simple Groups, Number 7: Chapters 7-11: the Generic Case, Stages 3b and 4a (Mathematical Surveys and Monographs) (Mathematical Surveys and Monographs, 40-7) - Hardcover

Daniel Gorenstein; Richard Lyons; Ronald Solomon

Hardcover

ISBN 10: 082184069X ISBN 13: 9780821840696

Publisher: American Mathematical Society, 2018

Synopsis

The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1-40.7 and future volumes) represents the culmination of a century-long project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4-40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13.The book is suitable for graduate students and researchers interested in the theory of finite groups.

About this title

About the Author

Daniel Gorenstein and Richard Lyons, Rutgers University, Piscataway, NY.Ronald Solomon, The Ohio State University, Columbus, OH.

Review

The presentation is just perfect. It is a tough business to present a proof which runs over three volumes. The authors take the reader by the hand, tell her or him what they are doing, and why and how it fits into the general picture. Thus, even if you are not willing to follow all the details, it gives you a good picture what the authors are doing and why this eventually yields a proof of the so-called generic case. --Gernot Stroth, Mathematical Reviews

Edition details

• Publisher: American Mathematical Society
• Publication date: 2018
• ISBN 10: 082184069X
• ISBN 13: 9780821840696
• Binding: Hardcover
• Language: English
• Number of pages: 344