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
Methods of the classification of finite simple groups
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
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
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.