Signalizers and balance in groups of finite Morley rank

TL;DR

This paper advances the understanding of simple groups of finite Morley rank by establishing bounds on Prufer 2-rank for minimal counterexamples to a major conjecture, and discusses the limitations of current classification methods.

Contribution

It proves that minimal counterexamples to the Cherlin-Zilber Algebraicity Conjecture have Prufer 2-rank at most two, and analyzes the signalizer functor theory for large Lie rank groups.

Findings

Prufer 2-rank of minimal counterexamples is at most two

Signalizer functor theory applied to groups of Lie rank at least three

Current classification methods are insufficient for larger groups

Abstract

We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has Prufer 2-rank at most two. This article covers the signalizer functor theory and identifies the groups of Lie rank at least three; leaving the uniqueness case analysis to previous articles. This result signifies the end of the general methods used to handle large groups; hereafter each individual group PSL$_2$, PSL$_3$, PSp$_4$, and G$_2$ will require its own identification theorem.