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We prove a Jordan decomposition theorem for minimal connected simple groupsof finite Morley rank with non-trivial Weyl group. From this, we deduce aprecise structural description of Borel subgroups of this family of simplegroups. Along the way we prove a Tetrachotomy theorem that classifies minimalconnected simple groups. Some of the techniques that we develop help us obtaina simpler proof of a theorem of Burdges, Cherlin and Jaligot.

A Jordan decomposition for groups of finite Morley rank