On analogies between algebraic groups and groups of finite Morley rank

Abstract

We prove that in a connected group of finite Morley rank the centralizers of decent tori are connected. We then apply this result to the analysis of minimal connected simple groups of finite Morley rank. Our applications include general covering properties by Borel subgroups, the description of Weyl groups and the analysis of toral automorphisms.

Cited by in corpus (5)

• Involutive automorphisms of $N_{\circ }^{\circ }$ groups of finite Morley rank
• Groups of finite Morley rank with a generically sharply multiply transitive action
• The geometry of involutions in ranked groups with a TI-subgroup
• Quasi groupes de Frobenius dimensionnels
• Moufang sets of finite Morley rank of odd type