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Simple Groups of Finite Morley Rank

Tuna Altınel Université de Lyon 1, Villeurbanne, France
Alexandre V. Borovik Manchester University, Manchester, England
Gregory Cherlin Rutgers University, Piscataway, NJ
Available Formats:
Hardcover ISBN: 978-0-8218-4305-5
Product Code: SURV/145
List Price: $119.00 MAA Member Price:$107.10
AMS Member Price: $95.20 Electronic ISBN: 978-1-4704-1372-9 Product Code: SURV/145.E List Price:$112.00
MAA Member Price: $100.80 AMS Member Price:$89.60
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List Price: $178.50 MAA Member Price:$160.65
AMS Member Price: $142.80 Click above image for expanded view Simple Groups of Finite Morley Rank Tuna Altınel Université de Lyon 1, Villeurbanne, France Alexandre V. Borovik Manchester University, Manchester, England Gregory Cherlin Rutgers University, Piscataway, NJ Available Formats:  Hardcover ISBN: 978-0-8218-4305-5 Product Code: SURV/145  List Price:$119.00 MAA Member Price: $107.10 AMS Member Price:$95.20
 Electronic ISBN: 978-1-4704-1372-9 Product Code: SURV/145.E
 List Price: $112.00 MAA Member Price:$100.80 AMS Member Price: $89.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$178.50 MAA Member Price: $160.65 AMS Member Price:$142.80
• Book Details

Mathematical Surveys and Monographs
Volume: 1452008; 556 pp
MSC: Primary 03; 20;

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.

Graduate students and research mathematicians interested in group theory and model theory related to logic.

• Part A. Methods
• I. Tools
• II. $K$-groups and $L$-groups
• III. Specialized topics
• IV. Generic covering and conjugacy theorems
• Part B. Mixed type groups
• V. Mixed type
• Part C. Even type groups
• VI. Strong embedding and weak embedding
• VII. Standard components of type $\mathrm {SL}_2$
• VIII. The $C(G,T)$ theorem and a plan of attack
• IX. Quasithin groups
• X. Conclusion

• 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
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Volume: 1452008; 556 pp
MSC: Primary 03; 20;

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.

Graduate students and research mathematicians interested in group theory and model theory related to logic.

• Part A. Methods
• I. Tools
• II. $K$-groups and $L$-groups
• III. Specialized topics
• IV. Generic covering and conjugacy theorems
• Part B. Mixed type groups
• V. Mixed type
• Part C. Even type groups
• VI. Strong embedding and weak embedding
• VII. Standard components of type $\mathrm {SL}_2$
• VIII. The $C(G,T)$ theorem and a plan of attack
• IX. Quasithin groups
• X. Conclusion
• 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
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