A signalizer functor theorem for groups of finite Morley rank

Pseudo-tori and subtame groups of finite Morley rank

“…We recall that an abelian connected group A of finite Morley rank is indecomposable if it is not the sum of two proper definable subgroups; see [4]. If A 0 1, then A has a unique maximal proper definable connected subgroup JðAÞ, and if A ¼ 1 we define Jð1Þ ¼ 1.…”

Conjugacy of Carter Subgroups in Groups of Finite Morley Rank

“…In [4], J. Burdges introduced some analogues of algebraic unipotence for groups of finite Morley rank. In [9], we continued the analysis of these concepts.…”

“…In [9], we continued the analysis of these concepts. Here are just given the more general results used in the article, and we refer to [4], or [9], for a more complete introduction concerning these unipotence notions.…”

“…U 0,r -groups. For a notion analogous to unipotence in algebraic groups, Burdges [4] introduced the notions of reduced rank and U 0,r -groups.…”

“…In Section 2, some well-known results are mentionned. In Section 3, we discuss the concepts of unipotence introduced by J. Burdges into [4]. All our information on the structure of studied groups will be based on these concepts.…”