**Mathematical Surveys and Monographs** 2008; 556 pp; hardcover Volume: 145 ISBN-10: 0-8218-4305-2 ISBN-13: 978-0-8218-4305-5 List Price: US$112 Member Price: US$89.60 Order Code: SURV/145
| The book gives a detailed presentation of the classification of the simple groups of finite Morley rank which contain a nontrivial unipotent 2-subgroup. They are linear algebraic groups over algebraically closed fields of characteristic two. Although the story told in the book is inspired by the classification of the finite simple groups, it goes well beyond this source of inspiration. Not only do the techniques adapted from finite group theory cover, in an unusual combination, various portions of the three generations of approaches to finite simple groups, but model theoretic methods also play an unexpected role. The book contains a complete account of all this material, part of which has not been published. In addition, almost every general result about groups of finite Morley rank is exposed in detail and the book ends with a chapter where the authors provide a list of open problems in the relevant fields of mathematics. As a result, the book provides food for thought to finite group theorists, model theorists, and algebraic geometers who are interested in group theoretic problems. Readership Graduate students and research mathematicians interested in group theory and model theory related to logic. Reviews "Not only is the lengthy and difficult proof presented in a very efficient way, readable both by model theorists and by finite and algebraic group theorists, but also the whole story is told in an informative and elegant style." *-- Mathematical Reviews* |