Cherlin-Zilber conjecture

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The Cherlin-Zilber conjecture in model theory suggests that simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields.

It was put forth by Gregory Cherlin of Rutgers University in New Jersey, and Boris Zilber of University of Oxford. Jeffrey Burdges states that "In the last 15 years, the main line of attack on this problem has been Borovik’s program of transferring methods from finite group theory." This method depends critically on the classification of finite simple groups. A number of special cases of this conjecture have been proved. Work on finding counterexamples to the overall conjecture is also active.

[edit] References

• Jeffrey Burdges, The Bender method in groups of finite Morley rank

• Groups, Geometry, and Logic, CIRM, September 27 - October 1, 2004

• A. V. Borovik, ‘Tame groups of odd and even type’, Algebraic Groups and their Representations, (eds R. W. Carter and J. Saxl), NATO ASI Series C: Mathematical and Physical Sciences 517, (Kluwer Academic Publishers, Dordrecht, 1998), pp. 341–366.

• A. V. Borovik and A. Nesin, Groups of Finite Morley Rank (Oxford University Press, 1994).

• CiteSeer: Groups of mixed type (1997)