On Weyl groups in minimal simple groups of finite Morley rank

Abstract

We prove that generous non-nilpotent Borel subgroups of connected minimal simple groups of finite Morley rank are self-normalizing. We use this to introduce a uniform approach to the analysis of connected minimal simple groups of finite Morley rank through a case division incorporating four mutually exclusive classes of groups. We use these to analyze Carter subgroups and Weyl groups in connected minimal simple groups of finite Morley rank. Finally, the self-normalization theorem is applied to give a new proof of an important step in the classification of simple groups of finite Morley rank of odd type.