A Generic Identification Theorem for L∗-Groups of Finite Morley Rank

Even Type Conjecture. Let G be a simple group of finite Morley rank of even type. Then G is a Chevalley group over an algebraically closed field of characteristic two. See [16] for an informal introduction to the subject, [1] for a recent survey of the classification programme, and [17] for general background on groups of finite Morley rank. An infinite simple group G of finite Morley rank whose Sylow 2-subgroups are of bounded exponent is said to be of even type if its Sylow 2-subgroups are ∗This paper came about as a result of discussions during the second author’s visit to METU, Ankara, and during the programme on Model Theory at the Newton Institute, Cambridge. The first two authors thank TÜBİTAK 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.