On Groups of Finite Morley Rank with Weakly Embedded Subgroups

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

“…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. Proof.…”

“…The following result was proved in [3] though stated somewhat differently; our formulation comes from [4]. …”

“…Here F = Z α−4 Z α as in (3). As Q α acts trivially on U and FQ α = G α F/C F U G α /Q α is of type SL 2 .…”

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

“…Section 2.4) is a natural generalization of strong embedding and far more flexible in practice (see for example the rapid elimination of cores in 2-local subgroups at the end of [3]). Tameness will be discussed in Section 2.…”

“…The present paper, together with the ongoing work on pushing up and the global C G T theorem, constitutes the last in the series of papers laying the foundations of the analysis of tame groups of even type by providing some general tools which are mostly connected with fusion analysis. One of the main tools in proving Theorem 1.1, or any of the classification theorems of this type, is the following classification theorem: Fact 1.2 [3]. Let G be a simple, tame, K * -group of finite Morley rank of even type.…”