Rank 3 Bingo

We classify irreducible actions of connected groups of finite Morley rank on abelian groups of Morley rank 3

Binding groups, permutation groups and modules of finite Morley rank

Chapitre invité dans un ouvrage à paraître. N'a pas encore été relu par nos pairs.The present survey aims at being a list of Conjectures and Problems in an area of model-theoretic algebra wide open for research, not a list of known results. To keep the text compact, it focuses on structures of finite Morley rank, although the same questions can be asked about other classes of objects, for example, groups definable in ω-stable and o-minimal theories. In many cases, answers are not known even in the classical category of algebraic groups over algebraically closed fields

Signalizers and balance in groups of finite Morley rank

We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has Prufer 2-rank at most two. This article covers the signalizer functor theory and identifies the groups of Lie rank at least three; leaving the uniqueness case analysis to previous articles. This result signifies the end of the general methods used to handle large groups; hereafter each individual group PSL$_2$, PSL$_3$, PSp$_4$, and G$_2$ will require its own identification theorem

Model Theory and Groups

The aim of the workshop was to discuss the connections between model theory and group theory. Main topics have been the interaction between geometric group theory and model theory, the study of the asymptotic behaviour of geometric properties on groups, and the model theoretic investigations of groups of finite Morley rank around the Cherlin-Zilber Conjecture