The Bender method in groups of finite Morley rank

Abstract

Jaligot's Lemma states that the Fitting subgroups of distinct Borel subgroups do not intersect in a tame minimal simple groups of finite Morley. Such a strong result appears hopeless without tameness. Here we use the 0-unipotence theory to build a toolkit for the analysis of nonabelian intersections of Borel subgroups. As a demonstration, we show that any connected nilpotent subgroup of an intersection of Borel subgroups, in a nontame minimal simple group, must actually be abelian.