Structure of Borel subgroups in simple groups of finite Morley rank

Tuna Altinel (1) , Jeffrey Burdges (2) , Olivier Frécon (3)

1 AGL - Algèbre, géométrie, logique
2 ICJ - Institut Camille Jordan
3 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

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.

Domaines: Logique [math.LO]; Théorie des groupes [math.GR]

Tuna Altinel, Jeffrey Burdges, Olivier Frécon. Structure of Borel subgroups in simple groups of finite Morley rank. Israel Journal of Mathematics, 2015, 208 (1), pp.101-162. ⟨10.1007/s11856-015-1195-3⟩. ⟨hal-00872349⟩