Groupes de Rang de Morley Fini de Type Pair avec un Sous-groupe Faiblement Inclus

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

“…Theorem 1.1 can be rephrased more precisely as follows: under the stated hypotheses, omitting the tameness, G has a weakly embedded subgroup. After the present work was complete, Jaligot completed a proof of the generalization of Fact 1.2 in which the tameness hypothesis is dropped [18,19]. Taking this into account, we see that Theorem 1.1 is also valid without a tameness hypothesis and, as should now be clear, the proof of that form of Theorem 1.1 is in fact given in the present paper, modulo [18,19].…”

“…Standard components will be defined in Section 6. As in the case of Theorem 1.1, one may also drop the tameness hypothesis here, via ( [19,18]), using the arguments of the present paper without any further modification.…”

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

“…All we need from previous papers in the series are the main results of [4,21], reviewed in the next section. Modulo standard group theoretic facts and some general properties of groups of finite Morley rank the present paper is self-contained.…”

Small groups of finite Morley rank with involutions

“…Fix U a maximal 2-unipotent subgroup of One sees easily with the same kind of arguments that for any nontrivial 2- This shunts the most difficult part of the analysis, [Jal01b, Théorème 4.1], reducing essentially to the situation of [Jal01b,§3], with M • = B solvable by local…”

“…• solvability • (a rather undirect fact in the general case of [ABC08], but rather direct in the case of [Jal01b]). We leave to the reader the pleasure of accomplishing the final recognition of PSL 2 along the lines of arguments and the computations of [Jal01b, Théorème 3.1], using here the fact that all normalizers…”