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There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. Towards this end, the development of the theory of groups of finite Morley rank has achieved a good theory of Sylow 2-subgroups. It is now common practice to divide the Cherlin-Zilber conjecture into… (More)

Modern model theory can be viewed as a subject obsessed with notions of dimension, with the key examples furnished by linear dimension on the one hand, and the dimension of an algebraic variety (or, from another point of view, transcendences degree) on the other. There are several rigorous, and not always equivalent, notions of abstract dimension in use.… (More)

- 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 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)

A group of finite Morley rank is a group whose definable subsets have a notion of dimension satisfying several basic axioms [BN94, p. 57]. Such groups arise naturally in model theory; initially as א1-categorical groups, i.e. as groups determined up to isomorphism by their first order theory, and here the simple groups correspond exactly. More recently… (More)

- JEFFREY BURDGES
- 2005

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)

- 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)

- 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 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)

OF THE DISSERTATION Simple Groups of Finite Morley Rank of Odd and Degenerate Type by Jeffrey Burdges Dissertation Director: Professor Gregory Cherlin The present thesis aims to drive Borovik’s program towards its final endgame, and to lay out a plan for bringing it to a conclusion. Borovik’s program is an approach to the longstanding Algebraicity… (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.

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 the so-called Borovik program of transferring methods from… (More)