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Preprint Number 645

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645. Tuna Altinel, Jeffrey Burdges, Olivier Frécon
Structure of Borel subgroups in groups of finite Morley rank
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Submission date: 28 October 2013.

Abstract:

We study the structure of subgroups of minimal connected simple groups of finite Morley rank. We first establish a Jordan decomposition for a large family of minimal connected simple groups including those with a non-trivial Weyl group. We then show that definable, connected, solvable subgroups of such a simple group are the semi-direct product of their unipotent part extended by a maximal torus. This is an essential step in the proof of the main theorem which provides a precise structural description of Borel subgroups.

Mathematics Subject Classification: 20F11 (primary), 03C60, 03C45 (secondary)

Keywords and phrases: Minimal simple groups, Groups of finite Morley rank, Borel subgroups, Carter subgroups, Jordan Decomposition

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