Signalizers and balance in groups of finite Morley rank

Details Signalizers and balance in groups of finite Morley rank Signalizers and balance in groups of finite Morley rank

2007-11-27

arxiv.org/abs/0711.4210v2

Mathematics

Logic

Scientific paper

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.

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