On groups of finite Morley rank of even type

Simple L∗-groups of even type with weakly embedded subgroups

“…Already in [5,Theorem 1] we showed the following. This implies that O • 2 (M) is a Sylow • 2-subgroup of M, and in fact its unique Sylow • 2-subgroup, which already clarifies the situation notably.…”

“…As in [5] and [6], the following three results will play an important role in linearizing actions of various groups on elementary abelian 2-groups. …”

“…The present paper is one of a series aiming at an affirmative answer to this algebraicity conjecture in the particular case of the simple groups of finite Morley rank of even type. The method used is the analysis of L * -groups, initiated in [5] (see Section 2 below for definitions).…”

“…Indeed, the intended analysis of simple L * -groups of even type is modeled very closely on that of simple K * -groups of even type. With this in mind, an initial analysis of weak embedding was undertaken in [5] in the L * -context, and in [6], a first L * -characterization of PSL 2 in characteristic two, using the stronger notion of strongly embedded subgroup, was obtained under additional hypotheses.…”

A Generation Theorem for Groups of Finite Morley Rank

“…For this we must further exploit strong embedding in the manner of [Alt,§5], and also (in a different direction) [AC03,§5].…”