Jeffrey Burdges

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The algebraicity conjecture for simple groups of finite Morley rank, also known as the Cherlin-Zilber conjecture, states that simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields. In the last 15 years, the main line of attack on this problem has been Borovik’s program of transferring methods from finite group(More)
The Algebraicity Conjecture states that a simple group of finite Morley rank should be isomorphic with an algebraic group. A program initiated by Borovik aims at controlling the 2-local structure in a hypothetical minimal counterexample to the Algebraicity Conjecture. There is now a large body of work on this program. A fundamental division arises at the(More)
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(More)