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 Pr\"ufer p-rank at least 2, leading either to some p-strong embedding, or to the Pr\"ufer p-rank being exactly 2

Involutive automorphisms of N∘∘N_\circ^\circ groups of finite Morley rank

We classify a large class of small groups of finite Morley rank: $N_\circ^\circ$-groups which are the infinite analogues of Thompson's $N$-groups. More precisely, we constrain the $2$-structure of groups of finite Morley rank containing a definable, normal, non-soluble, $N_\circ^\circ$-subgroup

Embeddings and chains of free groups

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

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

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

Some rigid moieties of homogeneous graphs

Any countable Kn-free graph T embeds as a moiety into the universal homogeneous Kn-free graph Kn in such a way that every automorphism of T extends into a unique automorphism of Kn. Furthermore, there are 2ω such embeddings which are pairwise not conjugate under Aut(Kn)

Tame minimal simple groups of finite Morley rank

AbstractWe consider tame minimal simple groups of finite Morley rank and of odd type. We show that the Prüfer 2-rank of such a group is bounded by 2. We also find all potential nonalgebraic configurations; there are essentially four of them, and we delineate them with some precision

Small groups of finite Morley rank with involutions

International audienceBy analogy with Thompson's classification of nonsolvable finite N-groups, we classify groups of finite Morley rank with solvable local subgroups of even and mixed type. We also consider several aspects reminiscent of "small" groups of finite Morley rank of odd type