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Preprint Number 271

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271. Tuna Altinel, Jeffrey Burdges, Oliver Frécon
A Jordan decomposition for groups of finite Morley rank
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Submission date: 21 September 2010.

Abstract:

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

Mathematics Subject Classification: 03C60, 20G99

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