Tame minimal simple groups of finite Morley rank (Q1883047)

The paper is a contribution to the program aiming to prove the Cherlin-Zil'ber algebraicity conjecture: any infinite simple group of finite Morley rank is an algebraic group over an algebraically closed field. A group of finite Morley rank is said to be tame if does not interpret a bad field naturally. A simple group of finite Morley rank is called minimal simple if all its proper definable connected subgroups are solvable. A group of finite Morley rank is said to be of odd type if the connected component of any Sylow 2-subgroup of it is a nontrivial divisible Abelian 2-group. The main result: in any tame minimal simple group of odd type the Prüfer rank of the connected component of a Sylow 2-subgroup is bounded by 2. -- For the remaining cases, in which the Prüfer rank is 1 or 2, the groups are analyzed from various points of view, notably in terms of Borel subgroups; the potential non-algebraic configurations are delineated with some precision.