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In a connected group of finite Morley rank, if the Sylow 2-subgroups are finite then they are trivial. The proof involves a combination of model theoretic ideas with a device originating in black box group theory.

We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the " Weyl group. " These results are quickly finding extensive applications within the classification project.

- Jeffrey Burdges
- 2005

The algebraicity conjecture for simple groups of finite Morley rank, also known as the Cherlin-Zilber conjecture, states that simple groups of finite Mor-ley 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)

- JEFFREY BURDGES
- 2005

- Jeffrey Burdges
- 2005

The algebraicity conjecture for simple groups of finite Morley rank, also known as the Cherlin-Zilber conjecture, states that simple groups of finite Mor-ley 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)

- JEFFREY BURDGES
- 2005

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)

There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik's trichotomy theorem. The 'trichotomy' here is a case division of the generic minimal counterexamples within odd type, that is, groups with a large and… (More)

- Tuna Altınel, Jeffrey Burdges
- 1997

We prove that in a connected group of finite Morley rank the centralizers of decent tori are connected. We then apply this result to the analysis of minimal connected simple groups of finite Morley rank. Our applications include general covering properties by Borel subgroups, the description of Weyl groups and the analysis of toral automorphisms.