Small groups of finite Morley rank with a supertight automorphism

Let G be an infinite simple group of finite Morley rank and of Prüfer 2-rank 1 which admits a supertight automorphism α such that the fixed-point subgroup CG(αn) is pseudofinite for all integers n>0. The main result of this paper is the identification of G with PGL2(K) for some algebraically closed field K of characteristic ≠2.