Lie rank in groups of finite Morley rank with solvable local subgroups

We prove a general dichotomy theorem for groups of finite Morley rank with solvable local subgroups and of Prufer p-rank at least 2, leading either to some p-strong embedding, or to the Prufer p-rank being exactly 2.

Cartan subgroups of groups definable in o-minimal structures

We prove that groups definable in o-minimal structures have Cartan subgroups, and only finitely many conjugacy classes of such subgroups. We also delineate with precision how these subgroups cover the ambient group, in general very largely in terms of the dimension.

Small groups of finite Morley rank with involutions

We consider groups of finite Morley rank with solvable local subgroups of even and mixed types. We also consider miscellaneous aspects of small groups of finite Morley rank of odd type.

Cosets, genericity, and the Weyl group

We prove a non-generosity theorem for proper cosets in groups of finite Morley rank and elaborate on the theory of Weyl groups in this context.

Embeddings and chains of free groups

We build two non-abelian CSA-groups in which maximal abelian subgroups are conjugate and divisible.

Groups of finite Morley rank with solvable local subgroups

We lay down the fundations of the theory of groups of finite Morley rank in which local subgroups are solvable and we proceed to the local analysis of these groups. We prove the main Uniqueness Theorem, analogous to the Bender method in finite group theory, and derive its corollaries. We also consider homogeneous cases as well as torsion.