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Research > Task V: Simple groups of finite Morley rank

Task V: Simple groups of finite Morley rank


Morley rank is a model-theoretic notion of dimension. In the case of algebraic groups over algebraically closed fields, it coincides with algebraic dimension. The Cherlin-Zilber conjecture states that a simple (infinite) group of finite Morley rank is an algebraic group over an algebraically closed field, and is a central goal.
Methods of the classification of finite simple groups can be applied successfully to those infinite groups possessing a reasonable concept of dimension (such as Morley rank), and one attempts to relate the `generic finite simple groups' to simple groups of finite Morley rank.

List of specific problems

    V.1: Simple groups of finite Morley rank

a) Complete the classification in even characteristic case.
b) In odd type case, reduce the analysis to certain specific configurations under inductive assumptions; eliminate the inductive assumptions. Eliminate simple groups with large finite Sylow 2-subgroups.
c) Prove that bad fields in positive characteristic do not exist, if necessary under a plausible number-theoretic hypothesis, via a development of Lang-Weil estimates for definable sets in a locally finite bad field.
d) Apply FMR techniques in finite group theory.


Years 1 and 2, Years 3 and 4.

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