Abstract
There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. The most successful approach to this conjecture has been Borovik's program analyzing a minimal counterexample, or simple K ∗ -group. We show that a simple K ∗ -group of finite Morley rank and odd type is either algebraic of else has Prüfer rank at most two. This result signifies a switch from the general methods used to handle large groups, to the specilized methods which must be used to identify PSL 2 , PSL 3 , PSp 4 , and G 2 .
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