6 research outputs found
Rank 3 Bingo
We classify irreducible actions of connected groups of finite Morley rank on
abelian groups of Morley rank 3
Simple groups of Morley rank 5 are bad
By exploiting the geometry of involutions in -groups of finite
Morley rank, we show that any simple group of Morley rank is a bad group
all of whose proper definable connected subgroups are nilpotent of rank at most
. The main result is then used to catalog the nonsoluble connected groups of
Morley rank
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
Involutive automorphisms of groups of finite Morley rank
We classify a large class of small groups of finite Morley rank:
-groups which are the infinite analogues of Thompson's
-groups. More precisely, we constrain the -structure of groups of finite
Morley rank containing a definable, normal, non-soluble,
-subgroup