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MODNET
Research Training Network in Model Theory



TASK V -  SIMPLE GROUPS OF FINITE MORLEY RANK


Description

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.   


Progress