Submission date: 12 March 2007.

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 identification theorems will cover only individual groups.

Mathematics Subject Classification: 03C60, 20G99

Keywords and phrases: "signalizer functor" balance "Morley rank"

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