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A generic identification theorem for L*-groups of finite Morley rank

Journal of Algebra
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  • Logic
  • Mathematics


doi:10.1016/j.jalgebra.2007.10.012 Journal of Algebra 319 (2008) 50–76 A Generic Identification Theorem for L∗-groups of finite Morley rank ✩,✩✩ Ays¸e Berkman a,∗, Alexandre V. Borovik b, Jeffrey Burdges b, Gregory Cherlin c a Mathematics Department, METU, Ankara 06531, Turkey b School of Mathematics, The University of Manchester, Oxford Street, Manchester M13 9PL, United Kingdom c Department of Mathematics, Rutgers University, Hill Center, Piscataway, NJ 08854, USA Received 7 July 2005 Available online 8 November 2007 Communicated by Gernot Stroth Abstract This paper provides a method for identifying “sufficiently rich” simple groups of finite Morley rank with simple algebraic groups over algebraically closed fields. Special attention is given to the even type case, and the paper contains a number of structural results about simple groups of finite Morley rank and even type. © 2007 Elsevier Inc. All rights reserved. Keywords: Group of finite Morley rank; Algebraic group ✩ This paper came about as a result of discussions during the second author’s visit to METU, Ankara in 2004, and during the program on Model Theory at the Newton Institute, Cambridge in 2005. The first two authors thank TÜB˙ITAK and Newton Institute for financial support. ✩✩ The last two authors acknowledge the hospitality of Université Lyon I, and the financial support of the Newton Institute Model Theory Program and NSF Grant DMS-0100794. * Corresponding author. E-mail addresses: [email protected] (A. Berkman), [email protected] (A.V. Borovik), [email protected] (J. Burdges), [email protected] (G. Cherlin). 0021-8693/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jalgebra.2007.10.012 A. Berkman et al. / Journal of Algebra 319 (2008) 50–76 51 1. Introduction 1.1. The Even Type Conjecture: global strategy According to a long-standing and thoroughly unresolved conjecture in model theory due to Zilber

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