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An identification theorem for groups of finite Morley rank and even type

✍ Scribed by Ayşe Berkman; Alexandre V. Borovik

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
84 KB
Volume
266
Category
Article
ISSN
0021-8693

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✦ Synopsis

The paper contains a construction of a definable BN-pair in a simple group of finite Morley rank and even type with a sufficiently good system of 2-local parabolic subgroups. This provides 'the final identification theorem' for simple groups of finite Morley rank and even type.

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Conjecture 1 (Even Type Conjecture). Let G be a simple group of finite Morley rank of even type, with no infinite definable simple section of degenerate type. Then G is algebraic.

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This paper gives a partial answer to the Cherlin᎐Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main res