Groupes de type mixte

Abstract

We show that a minimal counterexample to the Cherlin᎐Zil'ber conjecture Ž . tame or not cannot be of mixed type. ᮊ

Tame minimal simple groups of finite Morley rank

“…Building on earlier work in [2] about tame K * -groups, it is shown in [19]: Fact 1.6 [2,19]. Let G be a simple infinite K * -group of finite Morley rank.…”

Pushing Up and C(G,T) in Groups of Finite Morley Rank of Even Type

“…By the definition of a K * -group G is either a K-group or a simple group. If it is a K-group then Proposition 5.21 in [2] and Fact 3.9 in [20] prove the statement. If it is a simple group then the arguments used to prove Proposition 2.33 in [3] show that the stabilizer of a connected component of G is weakly embedded in G. Then Fact 2.11 yields the stated identification.…”

Groups of Finite Morley Rank and Even Type with Strongly Closed Abelian Subgroups

“…The present paper is a sequel to [1,3] (and, ideally, also to [18]), but familiarity with those papers is not essential beyond the points recalled above. It should be noted that the study of the "even type" groups as an isolated case is justified by [2,17].…”